A371329 E.g.f. satisfies A(x) = (exp(x/(1 - A(x))) - 1)/(1 - A(x)).
0, 1, 5, 58, 1099, 28966, 978669, 40349478, 1964141687, 110251617526, 7010830858753, 498111156585670, 39106669556183475, 3362091299430435846, 314139422902048625717, 31696638229827506705254, 3434797595698979061279727, 397852853779288923308578966
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=1, n, (n+2*k-2)!/(n+k-1)!*stirling(n, k, 2));
Formula
a(n) = Sum_{k=1..n} (n+2*k-2)!/(n+k-1)! * Stirling2(n,k).
E.g.f.: Series_Reversion( (1 - x) * log(1 + x * (1 - x)) ). - Seiichi Manyama, Sep 08 2024