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A369266
Expansion of (1/x) * Series_Reversion( x * (1-x) / (1+x^3)^2 ).
3
1, 1, 2, 7, 24, 84, 313, 1209, 4769, 19166, 78253, 323570, 1352122, 5701467, 24229122, 103663575, 446163435, 1930390329, 8391341664, 36630504952, 160509484616, 705750073063, 3112865367660, 13769327908980, 61066953746400, 271488240652950, 1209671359828154
OFFSET
0,3
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+2,k) * binomial(2*n-3*k,n-3*k).
a(n) = (1/(n+1)) * [x^n] ( 1/(1-x) * (1+x^3)^2 )^(n+1). - Seiichi Manyama, Feb 14 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)/(1+x^3)^2)/x)
(PARI) a(n, s=3, t=2, u=1) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 18 2024
STATUS
approved