A383234 Expansion of e.g.f. f(x)^4 * log(f(x)), where f(x) = 1/(1 - 5*x)^(1/5).
0, 1, 13, 218, 4646, 121080, 3741144, 133863792, 5447294352, 248518603584, 12566268267840, 697632464382336, 42189230206182528, 2760816706845539328, 194381535085933095936, 14652311175996819978240, 1177370323796943823325184, 100466288729505689717809152
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=1, n, k*4^(k-1)*5^(n-k)*abs(stirling(n, k, 1)));
Formula
a(n) = Sum_{k=1..n} k * 4^(k-1) * 5^(n-k) * |Stirling1(n,k)|.
a(n) = 5^(n-1) * n! * Sum_{k=0..n-1} (-1)^k * binomial(-4/5,k)/(n-k).
a(n) = (10*n-7) * a(n-1) - (5*n-6)^2 * a(n-2) for n > 1.