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A372476
Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x-x^3) )^n.
0
1, 2, 10, 59, 366, 2332, 15127, 99388, 659262, 4405379, 29611120, 199986085, 1356018339, 9225340880, 62941829996, 430495159084, 2950754125870, 20263845589461, 139393311839827, 960318328961614, 6624842357972916, 45757925847607270, 316401673996278705
OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(3*n-2*k-1,n-3*k).
The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x) * (1-x-x^3) ). See A368931.
PROG
(PARI) a(n, s=3, t=1, u=1) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t+u+1)*n-(s-1)*k-1, n-s*k));
CROSSREFS
Sequence in context: A340987 A186758 A372415 * A262910 A370281 A351502
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 02 2024
STATUS
approved