A391677 a(n) = Sum_{k=0..n} (k+1) * 2^k * 3^(n-k) * binomial(k,n-k)^2.

1, 4, 24, 176, 1052, 6624, 41632, 256768, 1584912, 9738944, 59592704, 363733248, 2214201280, 13448074240, 81518607360, 493270777856, 2980106119424, 17979034113024, 108329663973376, 651968407662592, 3919659639290880, 23542448283262976, 141276707220119552

Offset

0,2

Links

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

Formula

G.f.: (1-2*x-6*x^2)/((1-2*x-6*x^2)^2 - 48*x^3)^(3/2).

Mathematica

Table[Sum[(k+1)*2^k*3^(n-k)*Binomial[k, n-k]^2, {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Dec 19 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (k+1)*2^k*3^(n-k)*binomial(k, n-k)^2);
(Magma) [&+[(k+1)*2^k*3^(n-k)*Binomial(k, n-k)^2: k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Dec 19 2025

Crossrefs

Cf. A108490, A391678.

Sequence in context: A032349 A215709 A381882 * A103334 A156017 A000309

Adjacent sequences: A391674 A391675 A391676 * A391678 A391679 A391680

Keyword

nonn

Author

Seiichi Manyama, Dec 16 2025

Status

approved