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Christopher Sellman from Greggs Wood in Tunbridge Wells has been jailed after being found guilty of manslaughter in March.
Tiffany Sellman Burdge was just 25 days old when she died after suffering heart failure and bleeding to the brain while alone with her father, Christopher Sellman, from Tunbridge Wells, for the first time.
Passing sentence at Inner London Crown Court, Mr Justice Bean told Sellman he treated his daughter ``roughly'' and unlawfully killed her.
The judge told Sellman: ``Your daughter, Tiffany, was left in your care for the first time when she was only one month old. Within an hour she was effectively dead.'' He went on: ``It seems you were playing a computer game and were annoyed
when she cried. You picked her up and slammed her down on to a padded changing mat with a view to changing her nappy.''
But the judge said the baby girl turned blue and, despite ``desperate and frantic'' attempts by the defendant and emergency services to save her, later died. The judge went on: ``You intended her no harm but you treated her roughly and unlawfully killed her.'' He said Sellman made up a story about having slipped and dropped her, which the jury did not believe.
The judge added that Tiffany was ``more than usually vulnerable because of a skull fracture she suffered at birth''. But he said: ``Any one-month-old baby is tiny, fragile and vulnerable.'' The judge added that he found Sellman was a devoted father who was thrilled to have a daughter and showed her no animosity before this incident. It was a ``single incident without pre-meditation'', he said.
Tiffany's death in November 2008 could have been prevented if information had been shared about the risk Sellman posed to children, a serious case review by Kent Safeguarding Children Board found.
Sellman, 24, had a conviction for assault, and hazard warning flags were placed against his name by authorities after he was cautioned for child neglect before he was found guilty of killing Tiffany. Two other children under his care had been taken away from him and a former partner in the past by children's social services following concerns about them.
Opportunities to protect Tiffany were missed by children's social services and health agencies, the report, published in March, found. Relatives twice sought to alert agencies that Sellman's partner, Pamela Burdge, was pregnant with Tiffany, but the information was not passed on and was never registered.
When asked for a comment on the sentence outside court, Ms Burdge, told reporters: ``Not a chance.''
Detective Chief Inspector David Chewter, of Kent Police, said: ``I'm pleased the courts found Sellman guilty for the death of a defenceless child.
``He has never been able to provide a consistent account of what happened to Tiffany.
``Pamela's life has been turned upside-down and, to this day, she continues to struggle with her terrible loss.''