A362431 E.g.f. satisfies A(x) = exp(x - x^4 * A(x)).

1, 1, 1, 1, -23, -239, -1439, -6719, 33601, 1536193, 24171841, 268424641, 1144566721, -47515765439, -1727426116415, -36344982098879, -481057514071679, 1197767242412161, 319851095455612801, 12145632936380316289, 293167011107091899521, 3520557699737168603521

Offset

0,5

Links

Table of n, a(n) for n=0..21.

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

Formula

E.g.f.: exp(x - LambertW(x^4 * exp(x))) = LambertW(x^4 * exp(x))/x^4.

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(x^4*exp(x)))))

Crossrefs

Cf. A362396, A362430.

Cf. A362393.

Sequence in context: A290425 A034986 A243449 * A087332 A159998 A268747

Adjacent sequences: A362428 A362429 A362430 * A362432 A362433 A362434

Keyword

sign

Author

Seiichi Manyama, Apr 20 2023

Status

approved