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

1,2

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).

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

Mathematica

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

Crossrefs

Cf. A000217, A213500, A213548.

Sequence in context: A280660 A268186 A253130 * A211060 A242514 A030182

Adjacent sequences: A213546 A213547 A213548 * A213550 A213551 A213552

Keyword

nonn,easy

Author

Clark Kimberling, Jun 16 2012

Status

approved