A009135 Expansion of e.g.f. cosh(log(1+x)*exp(x)).

1, 0, 1, 3, 12, 30, 180, 490, 5600, 8064, 276360, -575872, 22950576, -166106512, 3194871680, -38456524080, 663548916992, -10330038449792, 186243968575488, -3385894106098944, 66478140305126272, -1354838641265098752

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) ~ (-1)^n * n! / (2 * Gamma(exp(-1)) * n^(1 - exp(-1))). - Vaclav Kotesovec, Jul 28 2018

Mathematica

With[{nn=30}, CoefficientList[Series[Cosh[Log[1+x]*Exp[x]], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Nov 29 2011 *)

Prog

(PARI) x='x+O('x^30); Vec(serlaplace(cosh(log(1+x)*exp(x)))) \\ G. C. Greubel, Jul 28 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+x)*Exp(x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 28 2018

Crossrefs

Sequence in context: A352157 A293656 A131936 * A131740 A037237 A005718

Adjacent sequences: A009132 A009133 A009134 * A009136 A009137 A009138

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved