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A368965
Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x-x^2)^2 ).
7
1, 3, 17, 117, 895, 7309, 62410, 550431, 4975297, 45846977, 429095387, 4067760593, 38977419018, 376901628882, 3673226867356, 36043590216621, 355800292078095, 3530878133357175, 35205183620396571, 352505713454687599, 3543078943592291301
OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+k+1,k) * binomial(4*n-k+2,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
Cf. A368966.
Sequence in context: A367945 A074544 A165976 * A344553 A121572 A340993
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 10 2024
STATUS
approved