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Search: id:A000294
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| A000294 |
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G.f.: Product_{k >= 1} (1 - x^k)^(-k*(k+1)/2).
(Formerly M3393 N1372)
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+0
5
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| 1, 1, 4, 10, 26, 59, 141, 310, 692, 1483, 3162, 6583, 13602, 27613, 55579, 110445, 217554, 424148, 820294, 1572647, 2992892, 5652954, 10605608, 19765082, 36609945, 67405569, 123412204, 224728451, 407119735, 733878402, 1316631730
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of partitions of n if there are k(k+1)/2 kinds of k (k=1,2,...). E.g. a(3)=10 because we have six kinds of 3, three kinds of 2+1 because there are three kinds of 2 and 1+1+1+1. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 23 2005
Euler transform of the triangular numbers 1,3,6,10,...
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009: (Start)
Equals A028377: [1, 1, 3, 9, 19, 46, 100,...] convolved with the aerated
version of A000294: [1, 0, 1, 0, 4, 0, 10, 0, 26, 0, 59,...]. (End)
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
A. O. L. Atkin, P. Bratley, I. G. McDonald and J. K. S. McKay, Some computations for m-dimensional partitions, Proc. Camb. Phil. Soc., 63 (1967), 1097-1100.
R. Chandra, Tables of solid partitions, Proceedings of the Indian National Science Academy, 26 (1960), 134-139.
V. S. Nanda, Tables of solid partitions, Proceedings of the Indian National Science Academy, 19 (1953), 313-314.
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FORMULA
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a(n) = (1/(2*n))*Sum_{k=1..n} (sigma[2](k)+sigma[3](k))*a(n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 17 2002
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MAPLE
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with (numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d, j; if n=0 then 1 else add (add (d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: a:= etr (n-> n*(n+1)/2): seq (a(n), n=0..30); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 08 2008]
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CROSSREFS
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Cf. A000293, A007294, A082535.
A028377 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009]
Sequence in context: A001214 A022812 A000293 this_sequence A133086 A126358 A099234
Adjacent sequences: A000291 A000292 A000293 this_sequence A000295 A000296 A000297
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Aug 15 2002
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