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Search: id:A107107
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| A107107 |
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For each partition of n, calculate (dM2/dM3) where dM2 = A036039(p) and dM3 = A036040(p); then sum over all partitions of n. |
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+0
3
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| 1, 1, 2, 4, 11, 37, 168, 926, 6181, 47651, 418546, 4106264, 44537519, 528408261, 6807428748, 94588717554, 1409927483625, 22437711255279, 379674820846534, 6806486383431340, 128862216628864163, 2569080120361323721
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OFFSET
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0,3
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COMMENT
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Values for individual partitions (A107106) are factorials when all but one part of the partition has size one or two, but not usually in other cases.
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FORMULA
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For partition [<c_i^k_i>], the contribution to the sum is product_i (c_i - 1)!^k_i.
G.f.: 1/Product_{m>0} (1-(m-1)!*x^m). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 10 2007
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EXAMPLE
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For n = 6,
(120,144,90,40,90,120,15,40,45,15,1) / (1,6,15,10,15,60,15,20,45,15,1)
equals (120,24,6,4,6,2,1,2,1,1,1) so A107107(6) = 168
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CROSSREFS
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Cf. A000142, A036039, A000110, A036040, A107106, A102189.
Cf. A077365.
Sequence in context: A035098 A138301 A118182 this_sequence A101898 A065851 A013044
Adjacent sequences: A107104 A107105 A107106 this_sequence A107108 A107109 A107110
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KEYWORD
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easy,nonn
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AUTHOR
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Alford Arnold (Alford1940(AT)aol.com), May 12 2005
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EXTENSIONS
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Edited, corrected and extended by Frank Adams-Watters (FrankTAW(AT)netscape.net), Nov 3 2005
More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 10 2007
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