A378043 E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x) * A(x)^2 ).

1, 2, 13, 190, 4045, 116746, 4251289, 187255174, 9684799961, 575477786674, 38638577549701, 2893159369162030, 239045577899472997, 21604942464613062010, 2120362938300115706513, 224568728344893756230326, 25529660577970226603535793, 3100816199696659908092912866

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)^3)/2 ).

a(n) = n! * Sum_{k=0..n} (2*k+1)^(k-1) * binomial(3*k+1,n-k)/k!.

Prog

(PARI) a(n) = n!*sum(k=0, n, (2*k+1)^(k-1)*binomial(3*k+1, n-k)/k!);

Crossrefs

Cf. A378019, A378044.

Cf. A377894, A378045.

Cf. A377894.

Sequence in context: A378093 A226865 A062156 * A371318 A323209 A239994

Adjacent sequences: A378040 A378041 A378042 * A378044 A378045 A378046

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2024

Status

approved