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

1,2

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).

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.

Mathematica

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

Crossrefs

Cf. A213561, A213500.

Sequence in context: A019584 A356420 A289393 * A041622 A160765 A192511

Adjacent sequences: A213559 A213560 A213561 * A213563 A213564 A213565

Keyword

nonn,easy

Author

Clark Kimberling, Jun 18 2012

Status

approved