A213562 Principal diagonal of the convolution array A213561.

1, 18, 109, 407, 1152, 2723, 5670, 10746, 18939, 31504, 49995, 76297, 112658, 161721, 226556, 310692, 418149, 553470, 721753, 928683, 1180564, 1484351, 1847682, 2278910, 2787135, 3382236, 4074903, 4876669, 5799942, 6858037

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. A213561, A213500.

Programs

Mathematica

(See A213561.)
LinearRecurrence[{6,-15,20,-15,6,-1},{1,18,109,407,1152,2723},30] (* Harvey P. Dale, Nov 12 2014 *)

Formula

a(n) = (4/15)*n^5 + (11/24)*n^4 + (1/4)*n^3 + (1/24)*n^2 - (1/16)*n.

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 + 12*x + 16*x^2 + 3*x^3)/(1 - x)^6.