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A391832

a(n) = (1/4) * Sum_{k=0..n} (k+2) * 2^k * binomial(2*k+2,2*n-2*k+1).

1, 6, 30, 160, 824, 4112, 20240, 98432, 473648, 2260000, 10707872, 50428928, 236267264, 1101967872, 5119345152, 23699419136, 109371557120, 503331831296, 2310505584128, 10581929451520, 48363392444416, 220617599430656, 1004622677749760, 4567358720147456, 20733836929429504

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OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-16,16,-72,32,-64,64,-16).

FORMULA

G.f.: (1-2*x-2*x^2) / ((1-2*x-2*x^2)^2 - 16*x^3)^2.

a(n) = 8*a(n-1) - 16*a(n-2) + 16*a(n-3) - 72*a(n-4) + 32*a(n-5) - 64*a(n-6) + 64*a(n-7) - 16*a(n-8).

MATHEMATICA

CoefficientList[Series[(1-2*x-2*x^2)/((1-2*x-2*x^2)^2-16*x^3)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 03 2026 *)

PROG