A346746 -id:A346746 - cp's OEIS frontend

A346747 E.g.f.: exp( (x * exp(x) + sinh(x)) / 2 ).

1, 1, 2, 6, 20, 79, 357, 1783, 9788, 58361, 374581, 2571851, 18779928, 145163975, 1183028095, 10129297307, 90843458256, 851083079649, 8309588493841, 84370700833147, 889152061199144, 9709123938880103, 109677977422359703, 1279880472867083111, 15408386793144717536

Offset: 0

Ilya Gutkovskiy, Aug 01 2021

nonn

Exponential transform of A110654.

Cf. A000248, A003724, A110654, A346746, A346748.

nmax = 24; 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] Ceiling[k/2] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A110654(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

A346747 E.g.f.: exp( (x * exp(x) + sinh(x)) / 2 ).

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