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Search: id:A141153
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| A141153 |
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G.f.: A(x) = Sum_{n>=1} a(n-1)*x^(2*n)/(2*n) = log( Sum_{n>=0} a(n)*x^(2*n)/(n!*2^n) ). |
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1
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| 1, 1, 3, 31, 1609, 626097, 2407996027, 110977327013551, 71594581089754557777, 738994182797188307880872353, 137301106425308220881681919632979379, 510195974626378486585193070538567102152265599
(list; graph; listen)
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OFFSET
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2,3
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FORMULA
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a(n+1) = n!*Sum_{k=0..n} 2^(n-k)/k!*a(k)*a(n-k), (offset 0). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 08 2008
E.g.f.: Sum_{n>=0} a(n)*x^n/n! = exp( Sum_{n>=1} 2^(n-1)*a(n-1)*x^n/n ) (offset 0). [From Paul D. Hanna (pauldhanna(AT)juno.com), Aug 09 2009]
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EXAMPLE
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G.f.: A(x) = x^2/2 + x^4/4 + 3*x^6/6 + 31*x^8/8 + 1609*x^10/10 + 626097*x^12/12 +...
exp(A(x)) = 1 + x^2/2 + 3*x^4/8 + 31*x^6/48 + 1609*x^8/384 + 626097*x^10/3840 +...
Contribution from Paul D. Hanna (pauldhanna(AT)juno.com), Aug 09 2009: (Start)
E.g.f.: E(x) = 1 + x + 3x^2/2! + 31*x^3/3! + 1609*x^4/4! +...(offset 0);
E(x) = exp(1*x + 1*2*x^2/2 + 3*2^2*x^3/3 + 31*2^3*x^4/4 + 1609*2^4*x^5/5 +...) (End)
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PROGRAM
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(PARI) {a(n)=if(n==0, 1, n!*2^n*polcoeff(exp(sum(k=0, n-1, a(k)*x^(2*k+2)/(2*k+2))+O(x^(2*n+2))), 2*n))}
Contribution from Paul D. Hanna (pauldhanna(AT)juno.com), Aug 09 2009: (Start)
(PARI) /* E.g.f. exp(Sum_{n>=1} 2^(n-1)*a(n-1)*x^n/n) with offset 0: */
{a(n)=n!*polcoeff(exp(sum(m=1, n, 2^(m-1)*a(m-1)*x^m/m)+x*O(x^n)), n)} (End)
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CROSSREFS
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Sequence in context: A094579 A029729 A136584 this_sequence A144906 A081789 A066976
Adjacent sequences: A141150 A141151 A141152 this_sequence A141154 A141155 A141156
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 11 2008
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