A377826 E.g.f. satisfies A(x) = (1 + x) * exp(x * A(x)).
1, 2, 7, 49, 489, 6521, 108643, 2178107, 51084337, 1373054833, 41624314371, 1405311853595, 52299954524953, 2127347522554073, 93902399411048803, 4470613587492385051, 228362858274694209249, 12458393118650371672673, 722983769486947261178371
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, (k+1)^(k-1)*binomial(k+1, n-k)/k!);
Formula
E.g.f.: (1+x) * exp( -LambertW(-x*(1+x)) ).
E.g.f.: -LambertW(-x*(1+x))/x.
a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(k+1,n-k)/k!.
a(n) ~ sqrt(-2*sqrt(1 + 4*exp(-1)) + 2 + 8*exp(-1)) * 2^n * n^(n-1) / ((-1 + sqrt(1 + 4*exp(-1)))^(n+1) * exp(n - 1/2)). - Vaclav Kotesovec, Nov 09 2024