A346746 E.g.f.: exp( (x * exp(x) - sinh(x)) / 2 ).

1, 0, 1, 1, 5, 12, 58, 220, 1145, 5684, 33284, 198412, 1306355, 8945046, 65658392, 503505600, 4076565489, 34442610648, 304577372128, 2802673411280, 26840614943667, 266644080930194, 2745669007978680, 29243006731749200, 321810005123384617, 3653558357684804324

Offset: 0

Author

Ilya Gutkovskiy, Aug 01 2021

Keywords

• nonn

Comments

Exponential transform of A004526.

Crossrefs

Cf. A000248, A003724, A004526, A346747, A346748.

Programs

Mathematica

nmax = 25; CoefficientList[Series[Exp[(x Exp[x] - Sinh[x])/2], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] Floor[k/2] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 25}]

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A004526(k) * a(n-k).