A119373 A lower diagonal of pendular trinomial triangle A119369.

1, 2, 6, 20, 70, 253, 938, 3546, 13617, 52967, 208255, 826315, 3304456, 13304924, 53891402, 219442686, 897772983, 3688451380, 15211545938, 62950542636, 261329456566, 1087985751336, 4541524025769, 19003488710465, 79696345430789

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

G.f.: A(x) = B(x)^2/(1+x - x*B(x)) = B(x)^2*G(x) = B(x)*H(x), where B(x) is g.f. of A119370, G(x) is g.f. of A119371 and H(x) is g.f. of A119372.

G.f.: 8*(1+x)/( ((1+x^2) +sqrt((1+x^2)^2 -4*x*(1+x)))^2*(1+4*x+x^2 +sqrt((1+4*x+x^2)^2 -4*x*(1+x)*(3+2*x))) ).

Mathematica

CoefficientList[Series[8*(1+x)/( ((1+x^2) + Sqrt[(1+x^2)^2 -4*x*(1+x)])^2*(1 + 4*x +x^2 +Sqrt[(1+4*x+x^2)^2 -4*x*(1+x)*(3+2*x)])), {x, 0, 30}], x] (* G. C. Greubel, Mar 16 2021 *)

Prog

(PARI) {a(n)=polcoeff(8*(1+x)/((1+x^2)+sqrt((1+x^2)^2-4*x*(1+x)+x*O(x^n)))^2 /(1+4*x+x^2 + sqrt((1+4*x+x^2)^2 - 4*x*(1+x)*(3+2*x)+x*O(x^n))), n)}
(Sage)
def A119373_list(prec):
    P.<x> = PowerSeriesRing(QQ, prec)
    return P( 8*(1+x)/( ((1+x^2) +sqrt((1+x^2)^2 -4*x*(1+x)))^2*(1+4*x+x^2 +sqrt((1+4*x+x^2)^2 -4*x*(1+x)*(3+2*x))) ) ).list()
A119373_list(30) # G. C. Greubel, Mar 16 2021
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 30);
Coefficients(R!( 8*(1+x)/( ((1+x^2) +Sqrt((1+x^2)^2 -4*x*(1+x)))^2*(1+4*x+x^2 +Sqrt((1+4*x+x^2)^2 -4*x*(1+x)*(3+2*x))) ) )); // G. C. Greubel, Mar 16 2021

Crossrefs

Cf. A119369, A119370, A119371, A119372, A119374, A119375, A119376.

Sequence in context: A302646 A000984 A087433 * A360292 A151284 A049138

Adjacent sequences: A119370 A119371 A119372 * A119374 A119375 A119376

Keyword

nonn

Author

Paul D. Hanna, May 17 2006

Status

approved