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%I #8 Dec 31 2023 10:22:10
%S 0,1,3,6,11,15,36,-42,666,-5499,55705,-611754,7342413,-95449549,
%T 1336296066,-20044437930,320711010756,-5452087178007,98137569210111,
%U -1864613814984794,37292276299704735,-783137802293788809,17229031650463366448,-396267727960657413354
%N a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * binomial(k+3,4) / k!.
%F a(0) = 0; a(n) = -n*a(n-1) + binomial(n+3,4).
%F E.g.f.: x * (1+3*x/2+x^2/2+x^3/24) * exp(x) / (1+x).
%o (PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(x*sum(k=0, 3, binomial(3, k)*x^k/(k+1)!)*exp(x)/(1+x))))
%Y Cf. A009574, A368585, A368587.
%Y Cf. A368575.
%K sign,easy
%O 0,3
%A _Seiichi Manyama_, Dec 31 2023