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%I #8 Dec 31 2023 10:22:06
%S 0,1,4,9,20,26,96,-210,2472,-20961,211612,-2324729,27901116,
%T -362708320,5077925048,-76168864092,1218701840976,-20717931276243,
%U 372922762998708,-7085532496941803,141710649938878564,-2975923648716396714,65470320271760793488
%N a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * binomial(k+4,5) / k!.
%F a(0) = 0; a(n) = -n*a(n-1) + binomial(n+4,5).
%F E.g.f.: x * (1+2*x+x^2+x^3/6+x^4/120) * exp(x) / (1+x).
%o (PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(x*sum(k=0, 4, binomial(4, k)*x^k/(k+1)!)*exp(x)/(1+x))))
%Y Cf. A009574, A368585, A368586.
%Y Cf. A368576.
%K sign,easy
%O 0,3
%A _Seiichi Manyama_, Dec 31 2023
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