A382985 Coefficient of x^4 in expansion of (x+1) * (x+4) * ... * (x+3*n-2).
0, 0, 0, 0, 1, 35, 1005, 28700, 859369, 27458613, 941164860, 34617398640, 1364003226036, 57425577775852, 2575788307560104, 122732603903789880, 6194752323883374224, 330320189407442698000, 18560921582024101872576, 1096473082032417593216832
Offset: 0
Keywords
Programs
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PARI
a(n) = polcoef(prod(k=0, n-1, x+3*k+1), 4);
Formula
a(n) = Sum_{k=4..n} 3^(n-k) * binomial(k,4) * |Stirling1(n,k)|.
E.g.f.: f(x) * log(f(x))^4 / 24, where f(x) = 1/(1 - 3*x)^(1/3).