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A023003
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Number of partitions of n into parts of 4 kinds.
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6
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1, 4, 14, 40, 105, 252, 574, 1240, 2580, 5180, 10108, 19208, 35693, 64960, 116090, 203984, 353017, 602348, 1014580, 1688400, 2778517, 4524760, 7296752, 11658920, 18468245, 29015700, 45235414, 70005376, 107585845, 164245380, 249162620
(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 A010709. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 17 2008]
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..500
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)^4.
a(0)=1, a(n)=1/n*sum(k=0,n-1, 4*a(k)*sigma_1(n-k)) - Joerg Arndt, Feb 5 2011
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MAPLE
| with (numtheory): a:= proc(n) option remember; `if`(n=0, 1, add (add (d*4, 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)^4, n, x)), ", "))
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CROSSREFS
| Sequence in context: A160463 A121593 A160527 * A001872 A054443 A072674
Adjacent sequences: A023000 A023001 A023002 * A023004 A023005 A023006
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KEYWORD
| nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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