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E.g.f. 1/sqrt(1+2x+4x^2).
1

%I #16 Jan 30 2020 21:29:16

%S 1,-1,-1,21,-111,-345,14895,-143955,-760095,49774095,-699437025,

%T -5221460475,458621111025,-8457966542025,-81662774418225,

%U 8999266227076125,-205480756062957375,-2434383666448358625,322739182334471277375,-8786388514658364484875

%N E.g.f. 1/sqrt(1+2x+4x^2).

%C First column of A182826.

%F D-finite with recurrence: a(n) +(2n-1)*a(n-1) +4*(n-1)^2*a(n-2)=0. - _R. J. Mathar_, Nov 17 2011

%t Table[(-1)^n*2^n*n!*LegendreP[n, 1/2], {n, 0, 20}] (* _Vaclav Kotesovec_, May 06 2017 *)

%o (PARI) x='x+O('x^55); Vec(serlaplace(1/sqrt(1+2*x+4*x^2)))

%K sign,easy

%O 0,4

%A _Paul Barry_, Dec 05 2010