A362342 -id:A362342 - cp's OEIS frontend

A362340 a(n) = n! * Sum_{k=0..floor(n/2)} (-k/2)^k / (k! * (n-2*k)!).

1, 1, 0, -2, 7, 51, -239, -2435, 16353, 209377, -1826099, -28232379, 303020125, 5494172893, -70032035163, -1457369472299, 21512472563281, 505400696581905, -8478758871011807, -221971772323923263, 4171251104170567101, 120416449897739144941

Offset: 0

Seiichi Manyama, Apr 17 2023

sign

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

Cf. A069856, A362341, A362342.

Cf. A362276.

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(x^2/2))))

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

A362341 a(n) = n! * Sum_{k=0..floor(n/3)} (-k/6)^k / (k! * (n-3*k)!).

Original entry on oeis.org

1, 1, 1, 0, -3, -9, 21, 246, 1065, -4283, -67319, -397484, 2315941, 45914155, 343743037, -2623221054, -62980998639, -571382718039, 5391435590545, 152175023203432, 1622112809355661, -18232162910685569, -591788241447761819, -7247966654986009490

Offset: 0

Seiichi Manyama, Apr 17 2023

sign

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

Cf. A069856, A362340, A362342.

Cf. A351929, A362303, A362348.

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(x^3/6))))

E.g.f.: exp(x) / (1 + LambertW(x^3/6)).

cp's OEIS Frontend

A362340 a(n) = n! * Sum_{k=0..floor(n/2)} (-k/2)^k / (k! * (n-2*k)!).

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