OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..600
FORMULA
n*a(n) = (10*n+25)*a(n-1) - 21*(n+5)*a(n-2) for n > 1.
a(n) = (-1)^n * Sum_{k=0..n} 7^k * 3^(n-k) * binomial(-7/2,k) * binomial(-7/2,n-k).
a(n) = Sum_{k=0..n} (-4)^k * 3^(n-k) * binomial(-7/2,k) * binomial(n+6,n-k).
a(n) = Sum_{k=0..n} 4^k * 7^(n-k) * binomial(-7/2,k) * binomial(n+6,n-k).
a(n) = (binomial(n+6,3)/20) * A387276(n).
a(n) = (-1)^n * Sum_{k=0..n} 10^k * (21/10)^(n-k) * binomial(-7/2,k) * binomial(k,n-k).
MATHEMATICA
CoefficientList[Series[1/((1-3x)*(1-7*x))^(7/2), {x, 0, 33}], x] (* Vincenzo Librandi, Aug 26 2025 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(1/((1-3*x)*(1-7*x))^(7/2))
(Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1/((1-3*x) * (1-7*x))^(7/2); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // Vincenzo Librandi, Aug 26 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 24 2025
STATUS
approved
