A213834 Antidiagonal sums of the convolution array A213833.

1, 10, 46, 140, 335, 686, 1260, 2136, 3405, 5170, 7546, 10660, 14651, 19670, 25880, 33456, 42585, 53466, 66310, 81340, 98791, 118910, 141956, 168200, 197925, 231426, 269010, 310996, 357715, 409510, 466736

Offset: 1

Author

Clark Kimberling, Jul 04 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 (5,-10,10,-5,1).

Crossrefs

Cf. A213833.

Programs

Mathematica

(See A213833.)

Formula

a(n) = n*(n+1)*(3*n^2 - 2*n + 2)/6.

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 + 2*x)(1 + 3*x) and g(x) = (1-x)^5.