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A374598
Expansion of 1/sqrt(1 - 4*x - 8*x^3).
3
1, 2, 6, 24, 94, 372, 1508, 6192, 25638, 106908, 448356, 1889040, 7989676, 33902504, 144259944, 615330784, 2630199942, 11263613484, 48315367076, 207556060816, 892819376964, 3845161246424, 16578320962104, 71548426931616, 309070048163676, 1336223562436632
OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(n-2*k,k) * binomial(2*(n-2*k),n-2*k).
n*a(n) = 2*(2*n-1)*a(n-1) + 4*(2*n-3)*a(n-3).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x-8*x^3))
(PARI) a(n) = sum(k=0, n\3, 2^k*binomial(n-2*k, k)*binomial(2*(n-2*k), n-2*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 13 2024
STATUS
approved