A346977 E.g.f.: log( 1 + (exp(x) - 1)^5 / 5! ).

1, 15, 140, 1050, 6951, 42399, 239800, 1164570, 2553551, -54771717, -1384474728, -23286667950, -339924740609, -4554547609233, -56481301888144, -630768487283886, -5665064764515849, -18095553874845909, 924820173031946752, 35413415495503624986

Offset

5,2

Links

Table of n, a(n) for n=5..24.

Formula

a(n) = Stirling2(n,5) - (1/n) * Sum_{k=1..n-1} binomial(n,k) * Stirling2(n-k,5) * k * a(k).

a(n) ~ -(n-1)! * 2^(1+n) * 5^n * cos(n*arctan((2*arctan(sqrt(10 - 2*sqrt(5))/(1 + sqrt(5) + 2^(7/5)/15^(1/5)))) / log(1 + 3^(1/5)*5^(7/10)/2^(2/5) + 15^(1/5)/2^(2/5) + 2^(6/5)*15^(2/5)))) / (100*arctan(sqrt(10 - 2*sqrt(5))/(1 + sqrt(5) + 2^(7/5)/15^(1/5)))^2 + (5*log(1 + 3^(1/5)*5^(7/10)/2^(2/5) + 15^(1/5)/2^(2/5) + 2^(6/5)*15^(2/5)))^2)^(n/2). - Vaclav Kotesovec, Aug 10 2021

Mathematica

nmax = 24; CoefficientList[Series[Log[1 + (Exp[x] - 1)^5/5!], {x, 0, nmax}], x] Range[0, nmax]! // Drop[#, 5] &
a[n_] := a[n] = StirlingS2[n, 5] - (1/n) Sum[Binomial[n, k] StirlingS2[n - k, 5] k a[k], {k, 1, n - 1}]; Table[a[n], {n, 5, 24}]

Crossrefs

Cf. A000481, A327506, A346955, A346974, A346975, A346976.

Sequence in context: A035330 A002803 A354394 * A354398 A056281 A000481

Adjacent sequences: A346974 A346975 A346976 * A346978 A346979 A346980

Keyword

sign

Author

Ilya Gutkovskiy, Aug 09 2021

Status

approved