A006229 -id:A006229 - cp's OEIS frontend

A293020 a(n) = n! * [x^n] exp(n*tan(x)).

1, 1, 4, 33, 384, 5705, 103392, 2213225, 54648832, 1529006769, 47806489600, 1651929898641, 62514008358912, 2571311967708601, 114219516618117120, 5449390043986849305, 277913379747357786112, 15087434965491213149153, 868698417435317196816384, 52875073161897308106963585

Offset: 0

Ilya Gutkovskiy, Sep 28 2017

nonn

Cf. A006229, A133941.

Table[n! SeriesCoefficient[Exp[n Tan[x]], {x, 0, n}], {n, 0, 19}]

a(n) ~ c * d^n * n^n / exp(n), where d = 3.2897906634948022290195938576166779380... and c = 0.7144692216716261155107169918... - Vaclav Kotesovec, Oct 06 2017

A302579 Expansion of e.g.f. exp(cosh(x)/cos(x)-1) (even powers only).

Original entry on oeis.org

1, 2, 24, 632, 28784, 1991552, 193410624, 24993180032, 4134783110144, 850499728758272, 212579274719007744, 63381008507902595072, 22200896917210834817024, 9019985888570141052280832, 4204783981520054371872374784, 2228007853953954434037178007552

Offset: 0

Ilya Gutkovskiy, Apr 10 2018

nonn

			exp(cosh(x)/cos(x)-1) = 1 + 2*x^2/2! + 24*x^4/4! + 632*x^6/6! + 28784*x^8/8! + ...

N. J. A. Sloane, Transforms

Cf. A000795, A005046, A006229, A009234, A009253, A009254, A009274, A012853, A217502.

nmax = 15; Table[(CoefficientList[Series[Exp[Cosh[x]/Cos[x] - 1], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]

a(n) = (2*n)! * [x^(2*n)] exp(cosh(x)/cos(x)-1).

cp's OEIS Frontend

A293020 a(n) = n! * [x^n] exp(n*tan(x)).

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