A357393 E.g.f. satisfies A(x) = -log(1 - x * exp(3 * A(x))).
0, 1, 7, 110, 2730, 93024, 4037880, 213127200, 13253058000, 948964262400, 76899763100160, 6957624460550400, 695236239163065600, 76043127767523840000, 9036546669251861760000, 1159342449440429270016000, 159708538424128885551360000, 23512778013219939149561856000
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=1, n, (3*n)^(k-1)*abs(stirling(n, k, 1)));
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PARI
a(n) = sum(k=1, n, (4*n)^(k-1)*stirling(n, k, 1));
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PARI
a(n) = if(n==0, 0, (4*n-1)!/(3*n)!);
Formula
E.g.f. satisfies A(x) = log(1 + x * exp(4 * A(x))).
a(n) = Sum_{k=1..n} (3 * n)^(k-1) * |Stirling1(n,k)|.
a(n) = Sum_{k=1..n} (4 * n)^(k-1) * Stirling1(n,k).
a(n) = Product_{k=3*n+1..4*n-1} k = (4*n-1)!/(3*n)! for n > 0.
E.g.f.: Series_Reversion( exp(-4*x) * (exp(x) - 1) ). - Seiichi Manyama, Sep 10 2024