A378046 E.g.f. satisfies A(x) = (1+x) * exp(x * A(x)^3 / (1+x)^2).
1, 2, 11, 169, 4049, 132881, 5542495, 280694135, 16730578625, 1147444968385, 89015365063991, 7707022678811567, 736734708409976017, 77070404075178587633, 8757816984586841345231, 1074244834335107678837191, 141469329806979182825146625, 19908315372027482035799282177
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Keywords
Links
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
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PARI
a(n) = n!*sum(k=0, n, (3*k+1)^(k-1)*binomial(k+1, n-k)/k!);
Formula
E.g.f.: (1+x) * exp( -LambertW(-3*x*(1+x))/3 ).
a(n) = n! * Sum_{k=0..n} (3*k+1)^(k-1) * binomial(k+1,n-k)/k!.