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A137957
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G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^4)^3.
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5
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1, 1, 3, 15, 79, 468, 2895, 18670, 123765, 838860, 5785503, 40473729, 286504086, 2048388112, 14770313397, 107290913232, 784380664232, 5766985753620, 42614014459911, 316304429143995, 2357275139670183, 17631888703154172
(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 A137958.
a(n) = Sum_{k=0..n-1} C(3*(n-k),k)/(n-k) * C(4*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^4)^3); polcoeff(A, n)}
(PARI) a(n)=if(n==0, 1, sum(k=0, n-1, binomial(3*(n-k), k)/(n-k)*binomial(4*k, n-k-1))) [From Paul D. Hanna (pauldhanna(AT)juno.com), Jun 16 2009]
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CROSSREFS
| Cf. A137958, A137956; A137953, A137962, A137969.
Sequence in context: A186942 A193913 A052755 * A002514 A093889 A020044
Adjacent sequences: A137954 A137955 A137956 * A137958 A137959 A137960
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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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