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A137961
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G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^2)^5.
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5
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1, 1, 5, 20, 105, 575, 3306, 19760, 121035, 757230, 4815530, 31039402, 202335855, 1331569725, 8834918160, 59035907480, 396937508816, 2683518356850, 18230570856710, 124390574548960, 852074529347120, 5857453791938135
(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)^5 where B(x) is the g.f. of A137960.
a(n) = Sum_{k=0..n-1} C(5*(n-k),k)/(n-k) * C(2*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^2)^5); polcoeff(A, n)}
(PARI) a(n)=if(n==0, 1, sum(k=0, n-1, binomial(5*(n-k), k)/(n-k)*binomial(2*k, n-k-1))) [From Paul D. Hanna (pauldhanna(AT)juno.com), Jun 16 2009]
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CROSSREFS
| Cf. A137960, A137962; A137963, A137965, A137973.
Sequence in context: A092640 A165961 A109500 * A167145 A020039 A117736
Adjacent sequences: A137958 A137959 A137960 * A137962 A137963 A137964
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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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