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A370107
Expansion of (1/x) * Series_Reversion( x / ((1-x)^2 * (1+x)^3) ).
2
1, 1, -1, -7, -10, 27, 152, 169, -949, -4286, -2646, 36499, 133684, -376, -1458768, -4325495, 3422105, 59242995, 139491393, -260949134, -2414487452, -4307455022, 15274866472, 97910544003, 119082795965, -805538039024, -3921641157424, -2408010178616, 40104318820288
OFFSET
0,4
FORMULA
G.f.: exp( Sum_{k>=1} A370106(k) * x^k/k ).
a(n) = (1/(n+1)) * Sum_{k=0..n} (-1)^k * binomial(2*(n+1),k) * binomial(3*(n+1),n-k).
a(n) = (1/(n+1)) * [x^n] ( (1-x)^2 * (1+x)^3 )^(n+1).
PROG
(PARI) a(n) = sum(k=0, n, (-1)^k * binomial(2*(n+1), k)*binomial(3*(n+1), n-k))/(n+1);
(PARI) my(x='x+O('x^30)); Vec(serreverse(x/((1-x)^2*(1+x)^3))/x) \\ Michel Marcus, Feb 10 2024
CROSSREFS
Cf. A370106.
Sequence in context: A064950 A240795 A058532 * A280966 A360430 A174466
KEYWORD
sign
AUTHOR
Seiichi Manyama, Feb 10 2024
STATUS
approved