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A137969
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G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^6)^3.
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5
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1, 1, 3, 21, 136, 1032, 8139, 66975, 567417, 4915386, 43350639, 387889254, 3512655498, 32133132074, 296496163113, 2756279003712, 25790064341592, 242699145598212, 2295564345035100, 21811226043019788, 208084639385653938
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| G.f.: A(x) = 1 + x*B(x)^3 where B(x) is the g.f. of A137970.
a(n) = Sum_{k=0..n-1} C(3*(n-k),k)/(n-k) * C(6*k,n-k-1) for n>0 with a(0)=1. [From Paul D. Hanna (pauldhanna(AT)juno.com), Jun 16 2009]
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PROG
| (PARI) {a(n)=local(A=1+x*O(x^n)); for(i=0, n, A=1+x*(1+x*A^6)^3); polcoeff(A, n)}
(PARI) a(n)=if(n==0, 1, sum(k=0, n-1, binomial(3*(n-k), k)/(n-k)*binomial(6*k, n-k-1))) [From Paul D. Hanna (pauldhanna(AT)juno.com), Jun 16 2009]
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CROSSREFS
| Cf. A137970, A137968; A137953, A137957, A137962.
Sequence in context: A124812 A141041 A079753 * A054419 A033888 A141492
Adjacent sequences: A137966 A137967 A137968 * A137970 A137971 A137972
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Feb 26 2008
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