A331608 E.g.f.: exp(1 / (1 - sinh(x)) - 1).

1, 1, 3, 14, 85, 632, 5559, 56352, 645929, 8252352, 116189291, 1786361216, 29764770941, 534082233856, 10264484355103, 210312181051392, 4575364233983057, 105310034714202112, 2556360647841415379, 65261358332774277120, 1747713179543456515749

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A006154(k) * a(n-k).

a(n) ~ exp(1/(2^(3/2) * log(1 + sqrt(2))) - 3/4 + 2^(3/4) * sqrt(n) / sqrt(log(1 + sqrt(2))) - n) * n^(n - 1/4) / (2^(5/8) * log(1 + sqrt(2))^(n + 1/4)). - Vaclav Kotesovec, Jan 27 2020

Mathematica

nmax = 20; CoefficientList[Series[Exp[1/(1 - Sinh[x]) - 1], {x, 0, nmax}], x] Range[0, nmax]!
A006154[n_] := Sum[Sum[(-1)^j (k - 2 j)^n Binomial[k, j]/2^k, {j, 0, k}], {k, 1, n}]; a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] A006154[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]

Crossrefs

Cf. A003704, A003724, A006154, A075729, A331607, A331611.

Sequence in context: A213628 A088716 A005189 * A331615 A317060 A308940

Adjacent sequences: A331605 A331606 A331607 * A331609 A331610 A331611

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 22 2020

Status

approved