A193385 Expansion of e.g.f. cosh( x^2/2 )/ (1-x).

1, 1, 2, 6, 27, 135, 810, 5670, 45465, 409185, 4091850, 45010350, 540134595, 7021749735, 98304496290, 1474567444350, 23593081136625, 401082379322625, 7219482827807250, 137170173728337750, 2743403475221484075

Offset: 0

Author

Michael Somos, Jul 24 2011

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..449

Crossrefs

Cf. A000266, A130905.

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(x^2/2)/(1-x))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 13 2018

Maple

a:=series(cosh(x^2/2)/(1-x),x=0,21): seq(n!*coeff(a,x,n),n=0..20); # Paolo P. Lava, Mar 27 2019

Mathematica

With[{nn=30},CoefficientList[Series[Cosh[x^2/2]/(1-x),{x,0,nn}], x] Range[0,nn]!] (* Harvey P. Dale, May 01 2012 *)

PARI

{a(n) = if( n<0, 0, n! * polcoeff( cosh( x^2 / 2 + x * O(x^n)) / (1 - x), n))}

Formula

a(n) ~ cosh( 1/2 ) * n!.

a(n) = (A000266(n) + A130905(n)) / 2.