A213818 Antidiagonal sums of the convolution array A213773.

1, 12, 60, 190, 465, 966, 1792, 3060, 4905, 7480, 10956, 15522, 21385, 28770, 37920, 49096, 62577, 78660, 97660, 119910, 145761, 175582, 209760, 248700, 292825, 342576, 398412, 460810, 530265, 607290, 692416

Offset: 1

Author

Clark Kimberling, Jul 04 2012

Keywords

• nonn
• easy

Links

• Clark Kimberling, Table of n, a(n) for n = 1..299
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A213773.

Programs

Mathematica

(See A213773.)

Formula

a(n) = (2*n - n^2 + 3*n^4)/4.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

G.f.: f(x)/g(x), where f(x) = x*(1 + 7*x + 10*x^2) and g(x) = (1-x)^5.

a(n) = A000217(n) * A005448(n). - John Elias, Jan 04 2022