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A369487
Expansion of (1/x) * Series_Reversion( x / (1-x) * (1-x-x^2)^3 ).
2
1, 2, 10, 57, 365, 2492, 17797, 131290, 992704, 7652558, 59918667, 475213662, 3809620760, 30820493162, 251309225465, 2063207320841, 17040385542611, 141487339935740, 1180337222858348, 9888553030497869, 83160409524964381, 701782096849536054
OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(3*n+k+2,k) * binomial(3*n-k+1,n-2*k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1-x)*(1-x-x^2)^3)/x)
(PARI) a(n, s=2, t=3, 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. A369488.
Sequence in context: A235321 A364306 A371770 * A248403 A278095 A075870
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 24 2024
STATUS
approved