A346747 -id:A346747 - cp's OEIS frontend

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

Ilya Gutkovskiy, Aug 01 2021

nonn

Exponential transform of A004526.

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

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}]

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

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

Original entry on oeis.org

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

Ilya Gutkovskiy, Aug 01 2021

sign

Exponential transform of A001057.

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

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}]

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

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

cp's OEIS Frontend

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

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