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A118970
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a(n) = 3*binomial(5n+2,n)/(4n+3).
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13
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1, 3, 18, 136, 1155, 10530, 100688, 996336, 10116873, 104819165, 1103722620, 11777187240, 127067830773, 1383914371728, 15194457001440, 167996704221280, 1868870731122405, 20903064321375315, 234927317665726686
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OFFSET
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0,2
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COMMENTS
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Convolved with A118969 (1, 2, 11, 80, 665, ...) = A002294: (1, 5, 35, 285, 2530, ...) - Gary W. Adamson, Nov 07 2011
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LINKS
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FORMULA
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8*n*(4*n+1)*(2*n+1)*(4*n+3)*a(n) -5*(5*n+1)*(5*n+2)*(5*n-2)*(5*n-1)*a(n-1)=0. - R. J. Mathar, Dec 02 2014
O.g.f. A(x) = (1/x) * series reversion ( x/C(x)^3 ), where C(x) = (1 - sqrt(1 - 4*x))/(2*x) is the o.g.f. for the Catalan numbers A000108.
(1/3)*x*A'(x)/A(x) = x + 9*x^2 + 91*x^3 + 969*x^4 + ... is the o.g.f. for A163456. (End)
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MAPLE
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ogf := series(RootOf(A = 1 + x * A^5, A)^3, x=0, 30); # Mark van Hoeij, Apr 22 2013
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MATHEMATICA
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PROG
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(PARI) a(n)=3*binomial(5*n+2, n)/(4*n+3); \\ Joerg Arndt, Apr 23 2013
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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