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Search: id:A134529
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| A134529 |
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E.g.f. A(x) satisfies: x/(1-x)^2 = Sum_{n>=1} (1/n!)*Prod_{j=0..n-1} A(2^j*x). |
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+0
1
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| 0, 1, 2, -8, -80, 1576, 43056, -4001376, -539274240, 230311875456, 169101315797760, -333305191377561600, -1205460382028665927680, 11038562078873652773729280, 187384458453666330945406187520, -7882186562442515869956999642009600
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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Define F(x,k,m) = Sum_{n>=1} (m*2^k)^n/n! * Product_{j=0..n-1} A(2^j*x), then F(x,k,m) is a series in x with integer coefficients for all integer m, k>=0.
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EXAMPLE
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E.g.f.: A(x) = x +2x^2/2! -8x^3/3! -80x^4/4! +1576x^5/5! +43056x^6/6! +...
where A(x) satisfies:
x/(1-x)^2 = A(x) + A(x)*A(2*x)/2! + A(x)*A(2*x)*A(2^2*x)/3! + A(x)*A(2*x)*A(2^2*x)*A(2^3*x)/4! + ...
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PROGRAM
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(PARI) {a(n, q=2)=local(A=x/(1-x+x*O(x^n))^2); for(i=1, n, A=x/(1-x)^2/(1+sum(j=1, n, prod(k=1, j, subst(A, x, q^k*x))/(j+1)!))); return(n!*polcoeff(A, n))}
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CROSSREFS
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Sequence in context: A063528 A073561 A130530 this_sequence A134054 A134086 A013175
Adjacent sequences: A134526 A134527 A134528 this_sequence A134530 A134531 A134532
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KEYWORD
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sign
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Nov 23 2007
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