A391676 a(n) = Sum_{k=0..n} 2^k * binomial(k+2,2) * binomial(k,n-k)^2.

1, 6, 30, 176, 984, 5232, 27312, 140160, 707952, 3531168, 17428896, 85249536, 413738240, 1994390016, 9556560384, 45550854144, 216094481664, 1020830461440, 4804034860544, 22529730809856, 105326409295872, 490983551209472, 2282693571072000, 10586924652920832

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

G.f.: ((1-2*x-2*x^2)^2 + 8*x^3)/((1-2*x-2*x^2)^2 - 16*x^3)^(5/2).

Mathematica

Table[Sum[2^k* Binomial[k+2, 2]*Binomial[k, n-k]^2, {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Dec 19 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, 2^k*binomial(k+2, 2)*binomial(k, n-k)^2);
(Magma) [&+[2^k*Binomial(k+2, 2)*Binomial(k, n-k)^2: k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Dec 19 2025

Crossrefs

Cf. A375276, A390612.

Sequence in context: A365273 A110706 A001341 * A089896 A057754 A382844

Adjacent sequences: A391673 A391674 A391675 * A391677 A391678 A391679

Keyword

nonn

Author

Seiichi Manyama, Dec 16 2025

Status

approved