A378092 E.g.f. satisfies A(x) = exp( x * (1-x) * A(x)^2 ) / (1-x).
1, 2, 11, 118, 1993, 46386, 1376059, 49601014, 2104366513, 102717184546, 5670357524011, 349304240222070, 23754501885783673, 1767641331001915474, 142868173684094891803, 12463599550013379095926, 1167281368458948415748833, 116814664082977998388994370, 12440156205235958837516345419
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
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PARI
a(n) = n!*sum(k=0, n, (2*k+1)^(k-1)*binomial(n, k)/k!);
Formula
E.g.f.: exp( -LambertW(-2*x/(1-x))/2 )/(1-x).
a(n) = n! * Sum_{k=0..n} (2*k+1)^(k-1) * binomial(n,k)/k!.
a(n) ~ (1 + 2*exp(1))^(n + 3/2) * n^(n-1) / (2^(5/2) * exp(n+1)). - Vaclav Kotesovec, Aug 05 2025