A263249 Expansion of e.g.f.: 2*cos(r*x)^2 / (1 + cos(r*x)^2) where r = sqrt(2), even terms only.

1, -2, -8, 112, 9088, 310528, -14701568, -4554426368, -458243735552, 37024075153408, 29290212127670272, 6224109737622372352, -631398107821314670592, -1112417825593218314534912, -422420220419591934719295488, 41942640830461258871206838272, 165285368668709582104936440659968, 101410495525765825487306697440493568

Offset: 0

Author

Paul D. Hanna, Oct 13 2015

Keywords

• sign

Examples

			E.g.f.: A(x) = 1 - 2*x^2/2! - 8*x^4/4! + 112*x^6/6! + 9088*x^8/8! + 310528*x^10/10! - 14701568*x^12/12! - 4554426368*x^14/14! +...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..233

Crossrefs

Cf. A263246, A263247, A263248.

Programs

Mathematica

With[{nn=40},Take[CoefficientList[Series[(2 Cos[x*Sqrt[2]]^2)/(1+Cos[ x*Sqrt[2]]^2),{x,0,nn}],x] Range[0,nn]!,{1,-1,2}]] (* Harvey P. Dale, Mar 13 2018 *)

PARI

{a(n) = local(S=x,C=1,D=1,ox=O(x^(2*n+2))); for(i=1,2*n+1, S = intformal(C*D^2 +ox); C = 1 - intformal(S*D^2); D = 1 + intformal(S*C*D);); (2*n)!*polcoeff(C^2, 2*n)}
for(n=0,20,print1(a(n),", "))