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Search: id:A074707
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| A074707 |
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exp(Sum_{n>0} x^n/n^2) = Sum_{n>=0} a(n)*x^n/n!^2. |
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+0
1
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| 1, 1, 3, 19, 214, 3846, 102206, 3795758, 188648664, 12125977944, 980768153832, 97599402813672, 11728820086206576, 1675575398007779568, 280777781273956353648, 54556438705747006028016
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, second edition, Addison Wesley, pp. 464-466.
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FORMULA
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a(n)=n!^2/n*sum(k=0, n-1, a(k)/k!^2/(n-k)). a(n)/n!^2 = exp(Pi^2/6)/n^2 + O(log(n)/n^3). - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 11 2003
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PROGRAM
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(PARI) a(n)=if(n<2, 1, (n-1)!^2+n!^2/n*sum(k=1, n-1, a(k)/k!^2/(n-k)))
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CROSSREFS
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Sequence in context: A049056 A000275 A058165 this_sequence A135749 A005647 A001833
Adjacent sequences: A074704 A074705 A074706 this_sequence A074708 A074709 A074710
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 04 2002
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