A346974 E.g.f.: log( 1 + (exp(x) - 1)^2 / 2 ).

1, 3, 4, -15, -134, -357, 2374, 33645, 133186, -1288617, -24887906, -130115895, 1666879306, 40612637523, 262868197414, -4221449488635, -123802488449774, -952293015617937, 18497401668708334, 632675912865355425, 5622243546094977946, -128799294291220310997

Offset

2,2

Links

Table of n, a(n) for n=2..23.

Formula

a(n) = Stirling2(n,2) - (1/n) * Sum_{k=1..n-1} binomial(n,k) * Stirling2(n-k,2) * k * a(k).

a(n) ~ -n! * 2^(n+1) * cos(n*arctan(2*arctan(sqrt(2))/log(3))) / (n * (4*arctan(sqrt(2))^2 + log(3)^2)^(n/2)). - Vaclav Kotesovec, Aug 09 2021

Mathematica

nmax = 23; CoefficientList[Series[Log[1 + (Exp[x] - 1)^2/2], {x, 0, nmax}], x] Range[0, nmax]! // Drop[#, 2] &
a[n_] := a[n] = StirlingS2[n, 2] - (1/n) Sum[Binomial[n, k] StirlingS2[n - k, 2] k a[k], {k, 1, n - 1}]; Table[a[n], {n, 2, 23}]

Crossrefs

Cf. A000225, A003704, A060311, A346975, A346976, A346977.

Sequence in context: A171061 A331869 A115752 * A354395 A103095 A041325

Adjacent sequences: A346971 A346972 A346973 * A346975 A346976 A346977

Keyword

sign

Author

Ilya Gutkovskiy, Aug 09 2021

Status

approved