A190736 Diagonal sums of the Riordan matrix A121576.

1, 2, 7, 29, 139, 731, 4096, 24005, 145420, 903503, 5726290, 36878978, 240663403, 1587928511, 10575884599, 71005972250, 480071241463, 3265685620913, 22335284505529, 153496543690226, 1059443187603955, 7340794592800628, 51042913856490028

Offset

0,2

Links

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

Formula

a(n) = [x^n](1-2*x-2*x^2)*(1+2*x)^(n+1)/((1+2*x-x^2+x^3)(1-x)^(n+1)).

G.f.: (4-5*x-2*x^2-(2+x)*sqrt(1-8*x+4*x^2))/(2*(1-x+2*x^2+x^3)).

Recurrence: 0 = 6*(n^2+17*n+72)*a(n+9) - (35*n^2+577*n+2376)*a(n+8) - (81*n^2+835*n+1856)*a(n+7) + (101*n^2+1017*n+2164)*a(n+6) - 2*(151*n^2+1883*n+5970)*a(n+5) - 2*(33*n^2+458*n+1528)*a(n+4) + (47*n^2+567*n+1564)*a(n+3) - 2*(7*n^2-16*n-120)*a(n+2) + 4*(3*n^2+8*n+4)*a(n+1) + 8*(n^2+3*n+2)*a(n).

Conjecture: n*(11*n-35)*a(n) + 3*(-33*n^2+149*n-136)*a(n-1) +2*(77*n^2-377*n+396)*a(n-2) +(-209*n^2+1061*n-1200)*a(n-3) +12*(-11*n+30)*a(n-4) +4*(11*n-24)*(n-4)*a(n-5)=0. - R. J. Mathar, Jul 24 2012

Mathematica

CoefficientList[Series[(4-5x-2x^2-(2+x)Sqrt[1-8x+4x^2])/(2(1-x+2x^2 +x^3) ), {x, 0, 22}], x]

Prog

(PARI) x='x+O('x^30); Vec((4-5*x-2*x^2-(2+x)*sqrt(1-8*x+4*x^2))/(2*(1-x+2*x^2+x^3))) \\ G. C. Greubel, Apr 23 2018
(Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((4-5*x-2*x^2-(2+x)*Sqrt(1-8*x+4*x^2))/(2*(1-x+2*x^2+x^3)))); // G. C. Greubel, Apr 23 2018

Crossrefs

Cf. A121576.

Sequence in context: A307389 A104252 A018977 * A265000 A347431 A355254

Adjacent sequences: A190733 A190734 A190735 * A190737 A190738 A190739

Keyword

nonn

Author

Emanuele Munarini, May 18 2011

Status

approved