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A005758
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Partitions of n into parts of 12 kinds.
(Formerly M4854)
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4
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1, 12, 90, 520, 2535, 10908, 42614, 153960, 521235, 1669720, 5098938, 14931072, 42124380, 114945780, 304351020, 784087848, 1970043621, 4837060800, 11626305640, 27398234760, 63388751544, 144156086776, 322590526350
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Euler transform of A010851. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 17 2008]
Convolution square of A005758 = A006922: (1, 24, 324, 3200, 25650,...) [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009]
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..200
N. J. A. Sloane, Transforms [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 17 2008]
Index entries for expansions of Product_{k >= 1} (1-x^k)^m
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FORMULA
| G.f.: Product ( 1 - x^k )^(-12).
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MAPLE
| with (numtheory): a:= proc(n) option remember; `if`(n=0, 1, add (add (d*12, 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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MATHEMATICA
| CoefficientList[Series[1/QPochhammer[x, x]^12, {x, 0, 30}], x] (* From Harvey P. Dale, Apr 21 2011 *)
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CROSSREFS
| Cf. 12th column of A144064. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 17 2008]
A006922 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009]
Sequence in context: A203636 A121590 A186209 * A084485 A130072 A135158
Adjacent sequences: A005755 A005756 A005757 * A005759 A005760 A005761
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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