A391990 a(n) = Sum_{k=0..floor(n/2)} (k+1) * binomial(n,k) * binomial(n-k,k).

1, 1, 5, 13, 43, 131, 411, 1275, 3963, 12283, 38023, 117503, 362605, 1117429, 3439229, 10572957, 32468787, 99610515, 305313711, 935015271, 2861204529, 8749050009, 26734768305, 81642292977, 249169635477, 760033085301, 2317086294201, 7060538711905, 21504623121763

Offset

0,3

Links

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

Formula

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

Mathematica

CoefficientList[Series[((1-x)^2-2*x^2)/((1-x)^2-4*x^2)^(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=1, B=1, C=A*B, N=1, 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)^2 - 2*x^2) / ((1-x)^2 - 4*x^2)^(3/2)); // Vincenzo Librandi, Dec 31 2025

Crossrefs

Cf. A002426, A098473.

Sequence in context: A147259 A328740 A183315 * A183184 A394014 A115785

Adjacent sequences: A391987 A391988 A391989 * A391991 A391992 A391993

Keyword

nonn

Author

Seiichi Manyama, Dec 26 2025

Status

approved