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A137963
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G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^3)^5.
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5
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1, 1, 5, 25, 160, 1075, 7671, 56760, 431865, 3357790, 26558520, 213032988, 1728808700, 14168337265, 117096909495, 974842628790, 8167462511193, 68813778610350, 582675107162175, 4955767502292960, 42318868510894860
(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 A137962.
a(n) = Sum_{k=0..n-1} C(5*(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)^5); polcoeff(A, n)}
(PARI) a(n)=if(n==0, 1, sum(k=0, n-1, binomial(5*(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. A137962, A137964; A137961, A137965, A137973.
Sequence in context: A179324 A097145 A085644 * A144887 A181344 A134007
Adjacent sequences: A137960 A137961 A137962 * A137964 A137965 A137966
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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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