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A174315 a(n) = 3F0( -n,-n+1,-n+2;;-1)= n!*(n-1)!* 1F2(-n+2;2,3;-1)/2, where nFm(;;z) are generalized hypergeometric series. 0

%I

%S 1,7,97,2221,75721,3591211,225827617,18168156217,1819029079441,

%T 221716249326991,32313176619313921,5547478498197397477,

%U 1107802527495396486937,254557467773494382397811

%N a(n) = 3F0( -n,-n+1,-n+2;;-1)= n!*(n-1)!* 1F2(-n+2;2,3;-1)/2, where nFm(;;z) are generalized hypergeometric series.

%C Special values of hypergeometric functions.

%F The sequence a(n) can be obtained from the following three generating functions of hypergeometric type:

%F g1(t) = sum(a(n)*t^n/(n!*(n-1)!),n=2..infinity) = (t^2/(1-t))* 1F2(1;2,3;t/(1-t))/2

%F g2(t) = sum(a(n)*t^n/(n!*(n-1)!*(n-2)!), n=2..infinity) = exp(t)*t^2* 0F2(;2,3;t)/2

%F g3(t) = sum(a(n)*t^n/(n!*(n-1)!*(n-2)), n=3..infinity)

%F = t^2*(t/(6*(1-t))* 2F3(1,1;2,3,4;t/(1-t))-log(1-t))/2

%F Note the appearance of the factor (n-2) and not (n-2)! in the denominator of g3.

%K nonn

%O 2,2

%A _Karol A. Penson_ and Katarzyna Gorska (gorska(AT)lptmc.jussieu.fr), Mar 15 2010

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Last modified May 6 09:22 EDT 2021. Contains 343580 sequences. (Running on oeis4.)