A213549 Principal diagonal of the convolution array A213548.

1, 12, 53, 155, 360, 721, 1302, 2178, 3435, 5170, 7491, 10517, 14378, 19215, 25180, 32436, 41157, 51528, 63745, 78015, 94556, 113597, 135378, 160150, 188175, 219726, 255087, 294553, 338430, 387035, 440696, 499752, 564553, 635460

Offset: 1

Author

Clark Kimberling, Jun 16 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. A000217, A213500, A213548.

Programs

Mathematica

(See A213548.)
LinearRecurrence[{5,-10,10,-5,1},{1,12,53,155,360},40] (* Harvey P. Dale, Nov 20 2022 *)

Formula

G.f.: x*(1 + 7*x + 3*x^2)/(1 - x)^5.

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

a(n) = (11*n^4 + 14*n^3 + n^2 - 2*n)/24 = n*(n+1)*(11*n^2 + 3*n - 2)/24.

a(n) = Sum_{i=1..n} (n-i+1)*A000217(n+i-1), see A213548. - Bruno Berselli, Oct 05 2016