A346748 - OEIS

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

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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}]