A213559 Principal diagonal of the convolution array A213558.

1, 91, 1366, 9542, 43535, 151313, 435324, 1089804, 2452269, 5071495, 9794290, 17873362, 31098587, 51953981, 83802680, 131102232, 199652505, 296878515, 432150478, 617143390, 866238439, 1196968553, 1630510388, 2192225060

Offset

1,2

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

a(n) = (16/35)*n^7 + (1/2)*n^6 + (1/15)*n^3 - (1/42)*n.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8).

G.f.: x*(1 + 83*x + 666*x^2 + 1106*x^3 + 421*x^4 + 27*x^5)/(1 - x)^8

Mathematica

(See A213558.)
LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 91, 1366, 9542, 43535, 151313, 435324, 1089804}, 40] (* Harvey P. Dale, Oct 09 2016 *)

Crossrefs

Cf. A213558, A213500.

Sequence in context: A020316 A221815 A195221 * A120756 A027787 A333112

Adjacent sequences: A213556 A213557 A213558 * A213560 A213561 A213562

Keyword

nonn,easy

Author

Clark Kimberling, Jun 17 2012

Status

approved