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A137970
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G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^3)^6.
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5
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1, 1, 6, 33, 236, 1776, 14148, 117070, 995568, 8653068, 76508562, 686035674, 6223653276, 57018806567, 526802616954, 4902775644477, 45919926029588, 432511043009679, 4094087001128088, 38927025591433926, 371607779425490280
(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)^6 where B(x) is the g.f. of A137969.
a(n) = Sum_{k=0..n-1} C(6*(n-k),k)/(n-k) * C(3*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^3)^6); polcoeff(A, n)}
(PARI) a(n)=if(n==0, 1, sum(k=0, n-1, binomial(6*(n-k), k)/(n-k)*binomial(3*k, n-k-1))) [From Paul D. Hanna (pauldhanna(AT)juno.com), Jun 16 2009]
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CROSSREFS
| Cf. A137969, A137971; A137968, A137972, A137974.
Sequence in context: A012522 A012326 A112903 * A024079 A118094 A121376
Adjacent sequences: A137967 A137968 A137969 * A137971 A137972 A137973
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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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