A362397 E.g.f. satisfies A(x) = exp(x - 3*x^2/2 * A(x)).

1, 1, -2, -17, 10, 976, 3736, -106910, -1386020, 15470380, 562409596, -722342444, -275109171776, -2700252315656, 152965123673272, 4156435296446896, -80740805437063664, -5565174444376872368, 6196702378365183952, 7539582040570866254032

Offset

0,3

Links

Table of n, a(n) for n=0..19.

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

Formula

E.g.f.: exp(x - LambertW(3*x^2/2 * exp(x))) = 2 * LambertW(3*x^2/2 * exp(x))/(3*x^2).

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(3*x^2/2*exp(x)))))

Crossrefs

Column k=3 of A362394.

Cf. A362380.

Sequence in context: A370111 A057280 A055677 * A257466 A226291 A359437

Adjacent sequences: A362394 A362395 A362396 * A362398 A362399 A362400

Keyword

sign

Author

Seiichi Manyama, Apr 20 2023

Status

approved