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

Author

Clark Kimberling, Jun 17 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 (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A213558, A213500.

Programs

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 *)

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