0,3

Vincenzo Librandi, Table of n, a(n) for n = 0..600

a(n) = Sum_{k=0..n} 4^(n-k) * binomial(7*k/2,n-k).

D-finite with recurrence (-n+1)*a(n) +2*(-2*n+11)*a(n-1) +(n-1)*a(n-2) +2*(16*n-25)*a(n-3) +56*(8*n-17)*a(n-4) +224*(16*n-43)*a(n-5) +4480*(4*n-13)*a(n-6) +3584*(16*n-61)*a(n-7) +14336*(8*n-35)*a(n-8) +8192*(16*n-79)*a(n-9) +32768*(2*n-11)*a(n-10)=0. - R. J. Mathar, Apr 02 2025

Table[Sum[4^(n-k)* Binomial[7*k/2, n-k], {k, 0, n}], {n, 0, 28}] (* Vincenzo Librandi, May 16 2025 *)

(PARI) a(n) = sum(k=0, n, 4^(n-k)*binomial(7*k/2, n-k));

(Magma) R<x>:=PowerSeriesRing(Rationals(), 28); Coefficients(R!( 1/(1 - x*(1 + 4*x)^(7/2)))); // Vincenzo Librandi, May 16 2025

Cf. A362154, A382536, A382537.

Cf. A002423.

Sequence in context: A307158 A000973 A034266 * A087661 A381862 A319777

Adjacent sequences: A382535 A382536 A382537 * A382539 A382540 A382541

nonn,easy

Seiichi Manyama, Mar 31 2025

approved