A391985 a(n) = Sum_{k=0..floor(n/4)} (k+1) * 2^k * 3^(n-3*k) * binomial(n-2*k,k) * binomial(n-3*k,k).

1, 3, 9, 27, 105, 459, 2025, 8667, 36369, 151875, 636417, 2679075, 11308761, 47779227, 201873465, 852827211, 3602606625, 15218565363, 64287833841, 271557920115, 1146975813225, 4843839405771, 20453167820457, 86349979376667, 364495327886385, 1538324367013539, 6491258197134561

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Formula

G.f.: ((1-3*x)^2 - 12*x^4) / ((1-3*x)^2 - 24*x^4)^(3/2).

Mathematica

CoefficientList[Series[((1-3*x)^2-12*x^4)/((1-3*x)^2-24*x^4)^(3/2), {x, 0, 50}], x] (* Vincenzo Librandi, Dec 31 2025 *)

Prog

(PARI) a098473(n, k) = binomial(n, k)*binomial(2*k, k);
my(A=2, B=3, C=A*B, N=1, M=30, x='x+O('x^M), X=1-B*x, Y=4); Vec(sum(k=0, N, (-C)^k*a098473(N, k)*X^(2*N-2*k)*x^(Y*k))/(X^2-4*C*x^Y)^(N+1/2))
(Magma) m := 50; R<x> := PowerSeriesRing(RationalField(), m); Coefficients(((1-3*x)^2 - 12*x^4) / ((1-3*x)^2 - 24*x^4)^(3/2)); // Vincenzo Librandi, Dec 31 2025

Crossrefs

Cf. A390830, A391986.

Cf. A098473, A098482.

Sequence in context: A325047 A148929 A148930 * A230951 A121746 A391986

Adjacent sequences: A391982 A391983 A391984 * A391986 A391987 A391988

Keyword

nonn

Author

Seiichi Manyama, Dec 26 2025

Status

approved