A327999 a(n) = Sum_{k=0..2n}(k!*(2n - k)!)/(floor(k/2)!*floor((2n - k)/2)!)^2.

1, 5, 28, 160, 896, 4864, 25600, 131072, 655360, 3211264, 15466496, 73400320, 343932928, 1593835520, 7314866176, 33285996544, 150323855360, 674309865472, 3006477107200, 13331578486784, 58823872086016, 258385232527360, 1130297953353728, 4925812092436480

Offset: 0

Author

Peter Luschny, Oct 01 2019

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (12,-48,64).

Crossrefs

Even bisection of A328000.

Programs

Mathematica

LinearRecurrence[{12, -48, 64}, {1, 5, 28}, 24] (* Michael De Vlieger, Feb 07 2020 *)

PARI

Vec((1 - 7*x + 16*x^2) / (1 - 4*x)^3 + O(x^25)) \\ Colin Barker, Feb 05 2020

PARI

apply( {A327999(n)=(n^2+n+8)<<(2*n-3)}, [0..25]) \\ M. F. Hasler, Feb 07 2020

Formula

a(n) = 4^n*(n^2 + n + 8)/8.

a(n) = [x^n] (-16*x^2 + 7*x - 1)/(4*x - 1)^3.

a(n) = n! [x^n] exp(4*x)*(2*x^2 + x + 1).

a(n) = a(n-1)*4*(8 + n + n^2)/(8 - n + n^2).

a(n) = A328000(2*n).

From Colin Barker, Feb 05 2020: (Start)

a(n) = 12*a(n-1) - 48*a(n-2) + 64*a(n-3) for n>2.

a(n) = 2^(2*n - 3)*(8 + n + n^2).

(End)