A368575 a(n) = n! * Sum_{k=0..n} binomial(k+3,4) / k!.
0, 1, 7, 36, 179, 965, 5916, 41622, 333306, 3000249, 30003205, 330036256, 3960436437, 51485675501, 720799459394, 10811991893970, 172991870307396, 2940861795230577, 52935512314156371, 1005774733968978364, 20115494679379576135, 422425388266971109461
Offset: 0
Programs
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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))))
Formula
a(0) = 0; a(n) = n*a(n-1) + binomial(n+3,4).
E.g.f.: x * (1+3*x/2+x^2/2+x^3/24) * exp(x) / (1-x).