OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
FORMULA
a(n) = Sum_{k=0..n} (-8)^k * binomial(-3/4,k) * binomial(n,k).
n*a(n) = (10*n-3)*a(n-1) - 9*(n-1)*a(n-2) for n > 1.
a(n) ~ Gamma(1/4) * 3^(2*n + 1/2) / (Pi * 2^(5/4) * n^(1/4)). - Vaclav Kotesovec, May 02 2025
a(n) = hypergeom([3/4, -n], [1], -8). - Stefano Spezia, May 05 2025
MATHEMATICA
Table[Sum[(-8)^k* Binomial[-3/4, k]* Binomial[n, k], {k, 0, n}], {n, 0, 22}] (* Vincenzo Librandi, May 05 2025 *)
PROG
(PARI) a(n) = sum(k=0, n, (-8)^k*binomial(-3/4, k)*binomial(n, k));
(Magma) R<x>:=PowerSeriesRing(Rationals(), 25); Coefficients(R!( 1/( (1-x) * (1-9*x)^3 )^(1/4))); // Vincenzo Librandi, May 05 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, May 01 2025
STATUS
approved