A377196 Expansion of 1/(1 - 4*x*(1+x)^2)^(7/2).
1, 14, 154, 1442, 12306, 98448, 751338, 5530800, 39567066, 276569216, 1896366472, 12793873820, 85126910050, 559668331068, 3641262380472, 23473114767228, 150084462238410, 952629409818492, 6006967242402280, 37653314869948316, 234749051092791928, 1456337836252645280
Offset: 0
Keywords
Programs
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Mathematica
a[n_]:=Sum[(-4)^k*Binomial[-7/2,k]Binomial[2*k,n-k],{k,0,n}]; Array[a,22,0] (* Stefano Spezia, May 08 2025 *) -
PARI
a(n) = sum(k=0, n, (-4)^k*binomial(-7/2, k)*binomial(2*k, n-k));
Formula
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.
a(n) = Sum_{k=0..n} (-4)^k * binomial(-7/2,k) * binomial(2*k,n-k).