A213565 Principal diagonal of the convolution array A213564.

1, 21, 127, 467, 1302, 3038, 6258, 11754, 20559, 33979, 53625, 81445, 119756, 171276, 239156, 327012, 438957, 579633, 754243, 968583, 1229074, 1542794, 1917510, 2361710, 2884635, 3496311, 4207581, 5030137, 5976552, 7060312

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 (6,-15,20,-15,6,-1).

Crossrefs

Cf. A213564, A213500.

Programs

Mathematica

(See A213564.)

Formula

a(n) = (16*n^5 + 85*n^4 + 15*n^3 - 25*n^2 - n)/60.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).

G.f.: x*(1 + 15*x + 16*x^2)/(1 - x)^6.