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A376159
G.f. satisfies A(x) = 1 / ((1-x)^3 - x*A(x)).
1
1, 4, 17, 90, 539, 3451, 23100, 159720, 1131905, 8178326, 60019533, 446166771, 3352530190, 25422458170, 194302002463, 1495223230621, 11575504625874, 90090318248607, 704480581789900, 5532228951823605, 43610427926723780, 344972119634359080, 2737451123900901555
OFFSET
0,2
FORMULA
G.f.: 2 / ((1-x)^3 + sqrt((1-x)^6 - 4*x)).
a(n) = Sum_{k=0..n} binomial(n+5*k+2,n-k) * binomial(2*k,k)/(k+1).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(2/((1-x)^3+sqrt((1-x)^6-4*x)))
(PARI) a(n) = sum(k=0, n, binomial(n+5*k+2, n-k)*binomial(2*k, k)/(k+1));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Sep 12 2024
STATUS
approved