A366589 G.f. A(x) satisfies A(x) = 1 + x^4*(1+x)*A(x)^2.
1, 0, 0, 0, 1, 1, 0, 0, 2, 4, 2, 0, 5, 15, 15, 5, 14, 56, 84, 56, 56, 210, 420, 420, 342, 834, 1980, 2640, 2409, 3795, 9141, 15015, 16445, 20449, 43043, 80509, 104962, 123838, 215072, 419848, 630838, 780572, 1164228, 2190552, 3629704, 4884100, 6760390, 11715210
Offset: 0
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 0..4920
Programs
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Maple
f:= gfun:-rectoproc({(10 + 4*n)*a(n) + (26 + 8*n)*a(n + 1) + (16 + 4*n)*a(n + 2) + (-10 - n)*a(n + 5) + (-10 - n)*a(n + 6) = 0, a(0) = 1, a(1) = 0, a(2) = 0, a(3) = 0, a(4) = 1, a(5) = 1},a(n),remember): map(f, [$0..30]); # Robert Israel, Oct 14 2024 -
PARI
a(n) = sum(k=0, n\4, binomial(k, n-4*k)*binomial(2*k, k)/(k+1));
Formula
G.f.: A(x) = 2 / (1+sqrt(1-4*x^4*(1+x))).
a(n) = Sum_{k=0..floor(n/4)} binomial(k,n-4*k) * binomial(2*k,k)/(k+1).
(10 + 4*n)*a(n) + (26 + 8*n)*a(n + 1) + (16 + 4*n)*a(n + 2) + (-10 - n)*a(n + 5) + (-10 - n)*a(n + 6) = 0. - Robert Israel, Oct 14 2024