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A376726
Expansion of (1 + x^2 - x^3)/((1 + x^2 - x^3)^2 - 4*x^2).
5
1, 0, 3, 1, 5, 10, 8, 35, 30, 85, 137, 201, 476, 616, 1357, 2172, 3735, 7193, 11213, 21782, 36064, 64095, 115130, 193769, 354737, 604049, 1074008, 1889968, 3273785, 5839608, 10106859, 17880785, 31325077, 54793282, 96710296, 168730043, 297336790, 520856765, 913684857
OFFSET
0,3
FORMULA
a(n) = 2*a(n-2) + 2*a(n-3) - a(n-4) + 2*a(n-5) - a(n-6).
a(n) = Sum_{k=0..floor(n/2)} binomial(2*k+1,2*n-4*k+1).
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec((1+x^2-x^3)/((1+x^2-x^3)^2-4*x^2))
(PARI) a(n) = sum(k=0, n\2, binomial(2*k+1, 2*n-4*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 03 2024
STATUS
approved