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Search: id:A161630
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| A161630 |
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E.g.f. satisfies: A(x) = exp( x/(1 - x*A(x)) ). |
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+0
3
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| 1, 1, 3, 19, 181, 2321, 37501, 731935, 16758393, 440525377, 13077834841, 432796650551, 15799794395749, 630773263606513, 27339525297079269, 1278550150117141231, 64171287394646697841, 3440711053857464325377
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(n) = Sum_{k=0..n} n! * (n-k+1)^(k-1)/k! * C(n-1,n-k).
Let A(x)^m = Sum_{n>=0} a(n,m)*x^n/n!, then
a(n,m) = Sum_{k=0..n} n! * m*(n-k+m)^(k-1)/k! * C(n-1,n-k).
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EXAMPLE
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E.g.f: A(x) = 1 + x + 3*x^2/2! + 19*x^3/3! + 181*x^4/4! + 2321*x^5/5! +...
log(A(x))/x = 1 + x*A(x) + x^2*A(x)^2 + x^3*A(x)^3 + x^4*A(x)^4 +...
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PROGRAM
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(PARI) {a(n, m=1)=if(n==0, 1, sum(k=0, n, n!/k!*m*(n-k+m)^(k-1)*binomial(n-1, n-k)))}
(PARI) {a(n, m=1)=local(A=1+x+x*O(x^n)); for(i=1, n, A=exp(x/(1-x*A))); n!*polcoeff(A^m, n)}
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CROSSREFS
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Cf. A125500.
Cf. A161633 (e.g.f. = log(A(x))/x). [From Paul D. Hanna (pauldhanna(AT)juno.com), Jun 23 2009]
Sequence in context: A045531 A129481 A156131 this_sequence A121083 A006531 A143633
Adjacent sequences: A161627 A161628 A161629 this_sequence A161631 A161632 A161633
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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 17 2009
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