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A372377
Expansion of (1/x) * Series_Reversion( x * (1+x)^2 / (1+x+x^3)^3 ).
3
1, 1, 1, 4, 13, 31, 91, 313, 988, 3095, 10377, 35146, 117682, 400117, 1381582, 4779997, 16599766, 58095076, 204319835, 720756820, 2552544940, 9074710255, 32356325145, 115679362789, 414701335849, 1490297002000, 5367227015647, 19369656905210, 70038419041844
OFFSET
0,4
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+3,k) * binomial(n-k+1,n-3*k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1+x)^2/(1+x+x^3)^3)/x)
(PARI) a(n, s=3, t=3, u=-2) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);
CROSSREFS
Sequence in context: A027998 A367010 A026567 * A218958 A226839 A270976
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 29 2024
STATUS
approved