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A023004
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Number of partitions of n into parts of 5 kinds.
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1
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) is Euler transform of A010716. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 17 2008]
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LINKS
| 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
| G.f.: Product_{m>=1} 1/(1-x^m)^5.
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MAPLE
| 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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PROG
| (PARI) \ps100 for(n=0, 100, print1((polcoeff(1/eta(x)^5, n, x)), ", "))
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CROSSREFS
| Cf. 5th column of A144064. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 17 2008]
Sequence in context: A100534 A160506 A160528 * A001873 A120297 A032286
Adjacent sequences: A023001 A023002 A023003 * A023005 A023006 A023007
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KEYWORD
| nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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