A378044 E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x) * A(x)^3 ).

1, 2, 17, 349, 10661, 444161, 23447635, 1500738989, 112954047113, 9777254959729, 956963374613471, 104510139881448797, 12599380858829314093, 1662018439019972570681, 238128379446158082330779, 36825779588890274967294061, 6113887910300601007096973585, 1084611999181162104894547358561

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(-3*x*(1+x)^4)/3 ).

a(n) = n! * Sum_{k=0..n} (3*k+1)^(k-1) * binomial(4*k+1,n-k)/k!.

Prog

(PARI) a(n) = n!*sum(k=0, n, (3*k+1)^(k-1)*binomial(4*k+1, n-k)/k!);

Crossrefs

Cf. A378019, A378043.

Cf. A377895.

Sequence in context: A204249 A242368 A307315 * A373324 A330260 A243509

Adjacent sequences: A378041 A378042 A378043 * A378045 A378046 A378047

Keyword

nonn,new

Author

Seiichi Manyama, Nov 15 2024

Status

approved