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A119374
A lower diagonal of pendular trinomial triangle A119369.
8
1, 3, 10, 36, 133, 501, 1918, 7440, 29180, 115522, 461044, 1852938, 7492846, 30464306, 124461782, 510696350, 2103708187, 8696498477, 36066269640, 150015248758, 625664295594, 2615929689642, 10962436020878, 46037427169060
OFFSET
0,2
LINKS
FORMULA
G.f.: A(x) = B(x)^3/(1+x - x*B(x)) = B(x)^3*G(x) = B(x)^2*H(x) = B(x)*I(x), where B(x) is g.f. of A119370, G(x) is g.f. of A119371, H(x) is g.f. of A119372 and I(x) is g.f. of A119373.
G.f.: 16*(1+x)/( ((1+x^2) +sqrt((1+x^2)^2-4*x*(1+x)))^3*(1+4*x+x^2 +sqrt((1+4*x+x^2)^2 - 4*x*(1+x)*(3+2*x))) ).
MATHEMATICA
CoefficientList[Series[16*(1+x)/( ((1+x^2) +Sqrt[(1+x^2)^2 -4*x*(1+x)])^3*(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(16*(1+x)/((1+x^2)+sqrt((1+x^2)^2-4*x*(1+x)+x*O(x^n)))^3 /(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 A119374_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( 16*(1+x)/( ((1+x^2) +sqrt((1+x^2)^2-4*x*(1+x)))^3*(1+4*x+x^2 +sqrt((1+4*x+x^2)^2 - 4*x*(1+x)*(3+2*x))) ) ).list()
A119374_list(30) # G. C. Greubel, Mar 16 2021
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 30);
Coefficients(R!( 16*(1+x)/( ((1+x^2) +Sqrt((1+x^2)^2-4*x*(1+x)))^3*(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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 17 2006
STATUS
approved