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A137958
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G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^3)^4.
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5
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1, 1, 4, 18, 100, 587, 3660, 23640, 157076, 1066281, 7363620, 51568732, 365369868, 2614235293, 18862816112, 137096744232, 1002785827620, 7376023180645, 54525165453672, 404858512190316, 3018190533410664, 22581907465905018
(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)^4 where B(x) is the g.f. of A137957.
a(n) = Sum_{k=0..n-1} C(4*(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)^4); polcoeff(A, n)}
(PARI) a(n)=if(n==0, 1, sum(k=0, n-1, binomial(4*(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. A137957, A137959; A137956, A137964, A137971.
Sequence in context: A197593 A084832 A135177 * A201826 A064852 A191365
Adjacent sequences: A137955 A137956 A137957 * A137959 A137960 A137961
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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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