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A229451
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G.f.: exp( Sum_{n>=1} (3*n)!/n!^3 * x^n/n ).
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1
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1, 6, 63, 866, 13899, 246366, 4676768, 93322596, 1934035965, 41286407510, 902562584556, 20119266633060, 455832458083577, 10470568749165246, 243361203186769659, 5714294570067499930, 135377464019074334826, 3232534121305720233264, 77726654423445817800164
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..18.
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FORMULA
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a(n) ~ c * 3^(3*n)/n^2, where c = 0.406436... - Vaclav Kotesovec, Dec 25 2013
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EXAMPLE
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G.f.: A(x) = 1 + 6*x + 63*x^2 + 866*x^3 + 13899*x^4 + 246366*x^5 +...
where
log(A(x)) = 6*x + 90*x^2/2 + 1680*x^3/3 + 34650*x^4/4 + 756756*x^5/5 +...+ A006480(n)*x^n/n +...
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MATHEMATICA
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CoefficientList[Series[Exp[6*x*HypergeometricPFQ[{1, 1, 4/3, 5/3}, {2, 2, 2}, 27*x]], {x, 0, 20}], x] (* Vaclav Kotesovec, Dec 25 2013 *)
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PROG
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(PARI) {a(n)=polcoeff(exp(sum(k=1, n, (3*k)!/k!^3*x^k/k) +x*O(x^n)), n)}
for(n=0, 25, print1(a(n), ", "))
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CROSSREFS
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Cf. A229452, A006480 (De Bruijn's S(3,n)).
Sequence in context: A234465 A231552 A302103 * A132078 A113669 A121415
Adjacent sequences: A229448 A229449 A229450 * A229452 A229453 A229454
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Sep 23 2013
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STATUS
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approved
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