A377894 E.g.f. satisfies A(x) = (1 + x) * exp(x * A(x)^2).

1, 2, 11, 142, 2725, 71026, 2339719, 93311758, 4371948137, 235418287042, 14327098759171, 972533690209390, 72854996624174989, 5970582808814848498, 531359818098465084863, 51034785131352404960686, 5261620527219949295345233, 579593410301187097865649922

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Eric Weisstein's World of Mathematics, Lambert W-Function.

Formula

E.g.f.: (1+x) * exp( -LambertW(-2*x*(1+x)^2)/2 ).

E.g.f.: ( -LambertW(-2*x*(1+x)^2)/(2*x) )^(1/2).

a(n) = n! * Sum_{k=0..n} (2*k+1)^(k-1) * binomial(2*k+1,n-k)/k!.

Prog

(PARI) a(n) = n!*sum(k=0, n, (2*k+1)^(k-1)*binomial(2*k+1, n-k)/k!);

Crossrefs

Cf. A377826, A377895.

Sequence in context: A177753 A183609 A113148 * A193209 A268743 A348797

Adjacent sequences: A377891 A377892 A377893 * A377895 A377896 A377897

Keyword

nonn

Author

Seiichi Manyama, Nov 11 2024

Status

approved