A216710 Expansion of (1-3*x+x^2)^2/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).

1, 3, 10, 35, 126, 460, 1690, 6225, 22950, 84626, 312019, 1150208, 4239225, 15621426, 57556155, 212037241, 781074572, 2877011660, 10596599460, 39027676220, 143735627861, 529352597361, 1949472483601, 7179308057596, 26438877143476, 97364252272077

Offset: 0

Author

Philippe Deléham, Apr 09 2013

Keywords

• nonn
• easy

Comments

A diagonal of the square array A223968.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-28,35,-15,1).

Crossrefs

Cf. A223968.

Programs

Mathematica

CoefficientList[Series[(1 - 3 x + x^2)^2/(1 - 9 x + 28 x^2 - 35 x^3 + 15 x^4 - x^5), {x, 0, 25}], x] (* Michael De Vlieger, Aug 19 2015 *)
LinearRecurrence[{9, -28, 35, -15, 1},{1, 3, 10, 35, 126},26] (* Ray Chandler, Aug 28 2015 *)

PARI

Vec((1-3*x+x^2)^2/(1-9*x+28*x^2-35*x^3+15*x^4-x^5) + O(x^30)) \\ Colin Barker, Aug 19 2015

Formula

a(n) = A223968(n,n+1).

G.f.: (1-3*x+x^2)^2/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).

a(n) = 9*a(n-1) - 28*a(n-2) + 35*a(n-3) - 15*a(n-4) + a(n-5) with a(0) = 1, a(1) = 3, a(2) = 10, a(3) = 35, a(4) = 126.