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%I #10 Dec 31 2023 10:22:48
%S 0,1,7,36,179,965,5916,41622,333306,3000249,30003205,330036256,
%T 3960436437,51485675501,720799459394,10811991893970,172991870307396,
%U 2940861795230577,52935512314156371,1005774733968978364,20115494679379576135,422425388266971109461
%N a(n) = n! * Sum_{k=0..n} 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. A007526, A103519, A368574, A368576.
%Y Cf. A000332, A337002.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, Dec 31 2023