A392032 a(n) = Sum_{k=0..floor(n/2)} binomial(k+2,2) * binomial(n,k) * binomial(n-k,k).

1, 1, 7, 19, 73, 241, 831, 2787, 9339, 31003, 102373, 336073, 1097911, 3570607, 11565529, 37324437, 120052107, 384962859, 1230978093, 3926097681, 12492150819, 39660238779, 125656218933, 397360559841, 1254333690477, 3952929646701, 12437932152051

Offset

0,3

Links

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

Formula

G.f.: ((1-x)^4 - 4*x^2*(1-x)^2 + 6*x^4) / ((1-x)^2 - 4*x^2)^(5/2).

Mathematica

CoefficientList[Series[((1-x)^4-4*x^2*(1-x)^2+6*x^4)/((1-x)^2-4*x^2)^(5/2), {x, 0, 50}], x] (* Vincenzo Librandi, Dec 31 2025 *)

Prog

(PARI) a098473(n, k) = binomial(n, k)*binomial(2*k, k);
my(A=1, B=1, C=A*B, N=2, M=30, x='x+O('x^M), X=1-B*x, Y=2); 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-x)^4 - 4*x^2*(1-x)^2 + 6*x^4) / ((1-x)^2 - 4*x^2)^(5/2)); // Vincenzo Librandi, Dec 31 2025

Crossrefs

Cf. A002426, A391990, A392033.

Cf. A098473.

Sequence in context: A318483 A005516 A152008 * A002533 A111011 A144723

Adjacent sequences: A392029 A392030 A392031 * A392033 A392034 A392035

Keyword

nonn

Author

Seiichi Manyama, Dec 27 2025

Status

approved