The OEIS is supported by the many generous donors to the OEIS Foundation.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #7 Oct 19 2024 08:31:31
%S 1,10,90,710,5250,37072,253330,1688640,11039370,71049200,451429880,
%T 2837585940,17674206130,109224234420,670398280520,4090210956596,
%U 24823230801450,149941593205140,901881446152120,5404072772837620,32269536034506456,192087243952281920
%N Expansion of 1/(1 - 4*x*(1+x)^2)^(5/2).
%F a(0) = 1, a(1) = 10, a(2) = 90; a(n) = (2*(2*n+3)*a(n-1) + 8*(n+3)*a(n-2) + 2*(2*n+9)*a(n-3))/n.
%F a(n) = Sum_{k=0..n} (-4)^k * binomial(-5/2,k) * binomial(2*k,n-k).
%o (PARI) a(n) = sum(k=0, n, (-4)^k*binomial(-5/2, k)*binomial(2*k, n-k));
%Y Cf. A137635, A377194, A377196.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Oct 19 2024