A346749 E.g.f.: exp( (x * (1 + x) * exp(x) - sinh(x)) / 4 ).

1, 0, 1, 2, 7, 26, 124, 628, 3565, 22096, 149176, 1080868, 8372543, 68957268, 601351748, 5528967282, 53416626441, 540682811424, 5718911631856, 63060992662328, 723382253378395, 8616075340134868, 106374847828850676, 1359171823319541070, 17946987240664242493

Offset: 0

Author

Ilya Gutkovskiy, Aug 01 2021

Keywords

• nonn

Comments

Exponential transform of A002620.

Crossrefs

Cf. A002620, A003724, A033462.

Programs

Mathematica

nmax = 24; CoefficientList[Series[Exp[(x (1 + x) Exp[x] - Sinh[x])/4], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] Floor[k^2/4] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A002620(k) * a(n-k).