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A136550
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a(n) = C(2^n + 2*n, n) * 2^n / (2^n + 2*n); a(n) = coefficient of x^n in Catalan(x)^(2^n).
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2
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1, 2, 14, 208, 7084, 648128, 184100160, 179176044032, 630345044388960, 8204566969800002560, 398166559635173802124288, 72163718410109803095272136704, 48857217948449362973220983661357056
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: A(x) = Sum_{n>=0} log( Catalan(2^n*x) )^n / n! where Catalan(x) = 2/(1+sqrt(1-4*x)).
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EXAMPLE
| G.f.: A(x) = 1 + 2*x + 14*x^2 + 208*x^3 + 7084*x^4 + 648128*x^5 +...
A(x) = Sum_{n>=0} log(1 +1*2^n*x +2*4^n*x^2 +5*8^n*x^3 +14*16^n*x^4 +...)^n/n!.
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PROG
| (PARI) {a(n)=binomial(2^n + 2*n, n)*2^n/(2^n + 2*n)} (PARI) {a(n)=polcoeff((2/(1+sqrt(1-4*x +x*O(x^n))))^(2^n), n)} (PARI) {a(n)=polcoeff(sum(k=0, n, log( 2/(1+sqrt(1-4*2^k*x +x*O(x^n))))^k/k!), n)}
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CROSSREFS
| Cf. A136551, A136552.
Sequence in context: A054652 A122647 A158097 * A068369 A034405 A197210
Adjacent sequences: A136547 A136548 A136549 * A136551 A136552 A136553
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jan 05 2008
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