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Search: id:A077365
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| A077365 |
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Sum of products of factorials of parts in all partitions of n. |
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+0
8
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| 1, 1, 3, 9, 37, 169, 981, 6429, 49669, 430861, 4208925, 45345165, 536229373, 6884917597, 95473049469, 1420609412637, 22580588347741, 381713065286173, 6837950790434781, 129378941557961565, 2578133190722896861
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OFFSET
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0,3
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COMMENT
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Row sums of arrays A069123 and A134133. Row sums of triangle A134134.
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FORMULA
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G.f.: 1/Product_{m>0} (1-m!*x^m). Recurrence: a(n) = 1/n*Sum_{k=1..n} b(k)*a(n-k), where b(k) = Sum_{d divides k} d*d!^(k/d).
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EXAMPLE
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The partitions of 4 are 4, 1+3, 2+2, 2+1+1, 1+1+1+1, the corresponding products of factorials of parts are 24,6,4,2,1 and their sum is a(4) = 37.
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CROSSREFS
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Cf. A006906, A074141.
Sequence in context: A134818 A002751 A119856 this_sequence A006229 A008986 A105215
Adjacent sequences: A077362 A077363 A077364 this_sequence A077366 A077367 A077368
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 30 2002
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EXTENSIONS
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Unnecessarily complicated mma code deleted by N. J. A. Sloane, Sep 21 2009
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