A213563 Antidiagonal sums of the convolution array A213561.

1, 10, 51, 182, 518, 1260, 2730, 5412, 9999, 17446, 29029, 46410, 71708, 107576, 157284, 224808, 314925, 433314, 586663, 782782, 1030722, 1340900, 1725230, 2197260, 2772315, 3467646, 4302585, 5298706, 6479992, 7873008, 9507080

Offset: 1

Author

Clark Kimberling, Jun 18 2012

Keywords

• nonn
• easy

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A213561, A213500.

Programs

Mathematica

(See A213561.)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,10,51,182,518,1260,2730},40] (* Harvey P. Dale, Aug 10 2024 *)

Formula

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).

G.f.: x*(1 + 3 x + 2*x^2)/(1 - x)^7.