A382984 Coefficient of x^3 in expansion of (x+1) * (x+4) * ... * (x+3*n-2).
0, 0, 0, 1, 22, 445, 9605, 227969, 5974388, 172323696, 5441287980, 187011672276, 6957458412520, 278765196526024, 11973706678705408, 549052544309039744, 26777325537157361024, 1384271732837081576576, 75622395021091990225152, 4353640204459556218940160
Offset: 0
Keywords
Programs
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PARI
a(n) = polcoef(prod(k=0, n-1, x+3*k+1), 3);
Formula
a(n) = Sum_{k=3..n} 3^(n-k) * binomial(k,3) * |Stirling1(n,k)|.
E.g.f.: f(x) * log(f(x))^3 / 6, where f(x) = 1/(1 - 3*x)^(1/3).