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A369486
Expansion of (1/x) * Series_Reversion( x / (1-x) * (1-x-x^2)^2 ).
2
1, 1, 4, 15, 67, 314, 1547, 7865, 41004, 217953, 1176832, 6436676, 35587416, 198569471, 1116741601, 6323669519, 36024382515, 206315985386, 1187205083042, 6860598312545, 39797882898452, 231666709974264, 1352813494962672, 7922553881534274, 46520280837291427
OFFSET
0,3
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+k+1,k) * binomial(2*n-k,n-2*k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1-x)*(1-x-x^2)^2)/x)
(PARI) a(n, s=2, t=2, u=1) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t-u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 24 2024
STATUS
approved