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

0,2

Links

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

Example

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! +...

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 *)

Prog

(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), ", "))

Crossrefs

Cf. A263246, A263247, A263248.

Sequence in context: A005787 A012343 A012347 * A297631 A099292 A284967

Adjacent sequences: A263246 A263247 A263248 * A263250 A263251 A263252

Keyword

sign

Author

Paul D. Hanna, Oct 13 2015

Status

approved