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Search: id:A023004
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| A023004 |
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Number of partitions of n into parts of 5 kinds. |
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+0
2
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| 1, 5, 20, 65, 190, 506, 1265, 2990, 6765, 14725, 31027, 63505, 126730, 247170, 472295, 885723, 1633000, 2963840, 5302075, 9358470, 16313440, 28107365, 47902010, 80803485, 134992865, 223474667, 366772720, 597049255, 964375855, 1546208695
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) is Euler transform of A010716. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 17 2008]
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LINKS
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Index entries for expansions of Product_{k >= 1} (1-x^k)^m
N. J. A. Sloane, Transforms [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 17 2008]
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FORMULA
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G.f.: Product_{m>=1} 1/(1-x^m)^5.
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MAPLE
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with (numtheory): a:=proc(n) option remember; `if`(n=0, 1, add (add (d*5, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq (a(n), n=0..40); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 17 2008]
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PROGRAM
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(PARI) \ps100 for(n=0, 100, print1((polcoeff(1/eta(x)^5, n, x)), ", "))
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CROSSREFS
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Cf. 5th column of A144064. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 17 2008]
Sequence in context: A011854 A001939 A100534 this_sequence A001873 A120297 A032286
Adjacent sequences: A023001 A023002 A023003 this_sequence A023005 A023006 A023007
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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