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A137967
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G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^6)^2.
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5
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1, 1, 2, 13, 66, 406, 2602, 17271, 118444, 829514, 5914980, 42791085, 313277294, 2316793170, 17281455882, 129867946828, 982293317064, 7472406051744, 57132051350160, 438797394096378, 3383870656327576, 26191385476141936
(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)^2 where B(x) is the g.f. of A137968.
a(n) = Sum_{k=0..n-1} C(2*(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)^2); polcoeff(A, n)}
(PARI) a(n)=if(n==0, 1, sum(k=0, n-1, binomial(2*(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. A137968, A137966; A137952, A137955, A137960.
Sequence in context: A160459 A037752 A037640 * A045764 A106999 A054566
Adjacent sequences: A137964 A137965 A137966 * A137968 A137969 A137970
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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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