A352906 Expansion of e.g.f. sinh(x) / (1 - sin(x)).

0, 1, 2, 7, 24, 101, 472, 2507, 14784, 96361, 687392, 5332207, 44694144, 402663821, 3880880512, 39848805107, 434306095104, 5007757446481, 60907946680832, 779345606053207, 10465549612529664, 147168296199468341, 2162785172079204352, 33155700678534788507, 529311396083558989824

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n,2*k+1) * A000111(n-2*k).

a(n) ~ sinh(Pi/2) * 2^(n + 7/2) * n^(n + 3/2) / (exp(n) * Pi^(n + 3/2)). - Vaclav Kotesovec, Apr 07 2022

Mathematica

nmax = 24; CoefficientList[Series[Sinh[x]/(1 - Sin[x]), {x, 0, nmax}], x] Range[0, nmax]!

Crossrefs

Cf. A000111, A000667, A000795, A001250, A002084, A062161, A062272, A322623, A348580.

Sequence in context: A150440 A150441 A150442 * A150443 A150444 A150445

Adjacent sequences: A352903 A352904 A352905 * A352907 A352908 A352909

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 07 2022

Status

approved