A277477 -id:A277477 - cp's OEIS frontend

A277475 E.g.f.: -sin(x)*LambertW(-x).

0, 0, 2, 6, 32, 300, 3576, 52234, 906688, 18229176, 416505760, 10657541422, 301871501568, 9375794555556, 316817746172032, 11570642333807730, 454152692297009152, 19064517871187079408, 852278820775206658560, 40424330665968520135382, 2027524052626732381306880

Offset: 0

Vaclav Kotesovec, Oct 17 2016

nonn

G. C. Greubel, Table of n, a(n) for n = 0..385

Cf. A000169, A277461, A277473, A277476, A277477.

CoefficientList[Series[-Sin[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
Table[Sum[Binomial[n, k] * Sin[Pi*(n-k)/2] * k^(k-1), {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 28 2016 *)

x='x+O('x^50); concat([0,0], Vec(serlaplace(-sin(x)*lambertw(-x)) )) \\ G. C. Greubel, Nov 07 2017

a(n) ~ sin(exp(-1)) * n^(n-1).

A277478 E.g.f.: -cosh(x)*LambertW(-x).

Original entry on oeis.org

0, 1, 2, 12, 76, 720, 8766, 131096, 2319416, 47361600, 1096018330, 28344108672, 810053677764, 25352185339520, 862335856149782, 31674845755622400, 1249527587684729584, 52687201308036059136, 2364751154207006978994, 112562199977955164819456

Offset: 0

Vaclav Kotesovec, Oct 17 2016

nonn

G. C. Greubel, Table of n, a(n) for n = 0..385

Cf. A000169, A277464, A277473, A277476, A277477.

CoefficientList[Series[-Cosh[x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
Table[Sum[(1 + (-1)^(n-k)) * Binomial[n, k] * k^(k-1)/2, {k, 1, n}], {n, 0, 20}]

x='x+O('x^50); concat([0], Vec(serlaplace(-cosh(x)*lambertw(-x)))) \\ G. C. Greubel, Nov 07 2017

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

a(n) ~ cosh(exp(-1)) * n^(n-1).

cp's OEIS Frontend

A277475 E.g.f.: -sin(x)*LambertW(-x).

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