A383231 Expansion of e.g.f. f(x) * log(f(x)), where f(x) = 1/(1 - 5*x)^(1/5).
0, 1, 7, 83, 1394, 30330, 810756, 25710012, 943434288, 39324264624, 1835297984160, 94813760519136, 5371462318747392, 331125138305434368, 22065681276731119104, 1580617232453691210240, 121117633854691036502016, 9885823380533972300470272, 856279708828545483688808448
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=1, n, k*5^(n-k)*abs(stirling(n, k, 1)));
Formula
a(n) = Sum_{k=1..n} k * 5^(n-k) * |Stirling1(n,k)|.
a(n) = 5^(n-1) * n! * Sum_{k=0..n-1} (-1)^k * binomial(-1/5,k)/(n-k).
a(n) = (10*n-13) * a(n-1) - (5*n-9)^2 * a(n-2) for n > 1.