A377196 - OEIS

%I #8 Oct 19 2024 08:31:35

%S 1,14,154,1442,12306,98448,751338,5530800,39567066,276569216,

%T 1896366472,12793873820,85126910050,559668331068,3641262380472,

%U 23473114767228,150084462238410,952629409818492,6006967242402280,37653314869948316,234749051092791928,1456337836252645280

%N Expansion of 1/(1 - 4*x*(1+x)^2)^(7/2).

%F a(0) = 1, a(1) = 14, a(2) = 154; a(n) = (2*(2*n+5)*a(n-1) + 8*(n+5)*a(n-2) + 2*(2*n+15)*a(n-3))/n.

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

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

%Y Cf. A137635, A377194, A377195.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 19 2024