Search: id:A000294
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%I A000294 M3393 N1372
%S A000294 1,1,4,10,26,59,141,310,692,1483,3162,6583,13602,27613,55579,110445,
%T A000294 217554,424148,820294,1572647,2992892,5652954,10605608,19765082,
%U A000294 36609945,67405569,123412204,224728451,407119735,733878402,1316631730
%N A000294 G.f.: Product_{k >= 1} (1 - x^k)^(-k*(k+1)/2).
%C A000294 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
%C A000294 Euler transform of the triangular numbers 1,3,6,10,...
%C A000294 Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009: 
               (Start)
%C A000294 Equals A028377: [1, 1, 3, 9, 19, 46, 100,...] convolved with the aerated
%C A000294 version of A000294: [1, 0, 1, 0, 4, 0, 10, 0, 26, 0, 59,...]. (End)
%D A000294 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000294 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000294 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.
%D A000294 R. Chandra, Tables of solid partitions, Proceedings of the Indian National 
               Science Academy, 26 (1960), 134-139.
%D A000294 V. S. Nanda, Tables of solid partitions, Proceedings of the Indian National 
               Science Academy, 19 (1953), 313-314.
%F A000294 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
%p A000294 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]
%Y A000294 Cf. A000293, A007294, A082535.
%Y A000294 A028377 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009]
%Y A000294 Sequence in context: A001214 A022812 A000293 this_sequence A133086 A126358 
               A099234
%Y A000294 Adjacent sequences: A000291 A000292 A000293 this_sequence A000295 A000296 
               A000297
%K A000294 nonn,easy
%O A000294 0,3
%A A000294 N. J. A. Sloane (njas(AT)research.att.com).
%E A000294 More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Aug 15 
               2002

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