A379456 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x) / (1 + x*exp(x)) ).
1, 2, 13, 151, 2573, 58221, 1648345, 56138461, 2236816825, 102135829609, 5259937376141, 301678137203433, 19072415186892325, 1317869007328182349, 98818139178323981473, 7991908824553634264101, 693473520767940388417265, 64266613784795934251538513
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, (2*n-k+1)^k*binomial(n+1, n-k)/k!)/(n+1);
Formula
a(n) = (n!/(n+1)) * Sum_{k=0..n} (2*n-k+1)^k * binomial(n+1,n-k)/k!.
E.g.f. A(x) satisfies A(x) = exp(x*A(x)) / ( 1 - x*exp(2*x*A(x)) ). - Seiichi Manyama, Feb 04 2025