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A369263
Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / (1+x^2)^3 ).
4
1, 2, 10, 54, 329, 2126, 14356, 100030, 713956, 5193064, 38354066, 286860714, 2168308302, 16537766036, 127114940840, 983657456878, 7657060437148, 59917814944376, 471062428422152, 3718952705982232, 29471640802526185, 234356062245289566, 1869405604537134116
OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(3*n+3,k) * binomial(3*n-2*k+1,n-2*k).
a(n) = (1/(n+1)) * [x^n] ( 1/(1-x)^2 * (1+x^2)^3 )^(n+1). - Seiichi Manyama, Feb 14 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2/(1+x^2)^3)/x)
(PARI) a(n, s=2, t=3, u=2) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);
CROSSREFS
Cf. A370245.
Sequence in context: A163909 A272178 A152395 * A365879 A202365 A330620
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 18 2024
STATUS
approved