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Search: id:A129587
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| A129587 |
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n!*( (1+3n+n^2)*H(n)-n ), where H=harmonic numbers. |
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3
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| 4, 29, 191, 1354, 10634, 92700, 892548, 9430416, 108630864, 1356063840, 18245210400, 263298142080, 4057825368960, 66527793642240, 1156298057913600, 21239191491840000, 411134620109875200, 8365635747476582400
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The numbers can be generated from row sums from coefficients of the polynomials sum_{i=1..n} [(n+1)^2-1+(n+1-i)*z^n]*z^(i-1)/i.
The coefficients written as an array of 2n numbers in row n for the first 5 polynomials are
3 1 <- 3+z
8 4 2 1/2 <- 8+4z+2z^2+z^3/2
15 15/2 5 3 1 1/3
24 12 8 6 4 3/2 2/3 1/4
35 35/2 35/3 35/4 7 5 2 1 1/2 1/5
These rows multiplied by n! are
3 1
16 8 4 1
90 45 30 18 6 2
576 288 192 144 96 36 16 6
4200 2100 1400 1050 840 600 240 120 60 24
where the first column is A129326. The latter row sums define a(n), which are n! times the polynomials evaluated at z=1.
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CROSSREFS
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Cf. A001008, A002805, A129326.
Sequence in context: A095670 A079885 A121191 this_sequence A143551 A100022 A001883
Adjacent sequences: A129584 A129585 A129586 this_sequence A129588 A129589 A129590
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KEYWORD
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nonn,less
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), May 30 2007
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EXTENSIONS
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Edited and corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 27 2008
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