A213748 Principal diagonal of the convolution array A213747.

1, 16, 125, 758, 4071, 20424, 98185, 458506, 2096651, 9436172, 41941005, 184545294, 805298191, 3489644560, 15032352785, 64424443922, 274877775891, 1168230842388, 4947801800725, 20890719879190, 87960928124951

Offset: 1

Author

Clark Kimberling, Jun 19 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 (12,-53,106,-96,32).

Crossrefs

Cf. A213747, A213500.

Programs

Mathematica

(See A213747.)
LinearRecurrence[{12,-53,106,-96,32},{1,16,125,758,4071},30] (* Harvey P. Dale, Aug 15 2012 *)

Formula

a(n) = 12*a(n-1) - 53*a(n-2) + 106*a(n-3) - 96*a(n-4) + 32*a(n-5).

G.f.: f(x)/g(x), where f(x) = x*(1 + 4*x - 14*x^2) and g(x) = (1 - 2*x)*(1 - 5*x + 4*x^2)^2.

a(n) = 2 - 2^n + 4^n*(n-1) + n. - Colin Barker, Nov 07 2017