A346748 E.g.f.: exp( (x * exp(-x) + sinh(x)) / 2 ).

1, 1, 0, 0, 4, -1, -9, 103, -132, -535, 7731, -25117, -18072, 1078215, -6917039, 16312667, 186611792, -2454241183, 14370311311, 1436259867, -934228834216, 10658996229479, -54990712418263, -185381404760729, 7270919988375200, -80130195880201583, 391992372213719679

Offset

0,5

Comments

Exponential transform of A001057.

Links

Table of n, a(n) for n=0..26.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A001057(k) * a(n-k).

Mathematica

nmax = 26; CoefficientList[Series[Exp[(x Exp[-x] + Sinh[x])/2], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[(-1)^(k + 1) Binomial[n - 1, k - 1] Floor[(k + 1)/2] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 26}]

Crossrefs

Cf. A001057, A003724, A003725, A346746, A346747.

Sequence in context: A348180 A176080 A328302 * A348184 A065045 A185088

Adjacent sequences: A346745 A346746 A346747 * A346749 A346750 A346751

Keyword

sign

Author

Ilya Gutkovskiy, Aug 01 2021

Extensions

Typo in a(26) corrected by Georg Fischer, Nov 30 2021

Status

approved