Search: id:A002621
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%I A002621 M1051 N0394
%S A002621 1,2,4,7,12,18,27,38,53,71,94,121,155,194,241,295,359,431,515,609,717,
%T A002621 837,973,1123,1292,1477,1683,1908,2157,2427,2724,3045,3396,3774,4185,
%U A002621 4626,5104,5615,6166,6754,7386,8058,8778,9542,10358,11222,12142,13114
%N A002621 Expansion of 1 / ((1-x)^2*(1-x^2)*(1-x^3)*(1-x^4)).
%D A002621 E. Fix and J. L. Hodges, Jr., Significance probabilities of the Wilcoxon 
               test, Annals Math. Stat., 26 (1955), 301-312.
%D A002621 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002621 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A002621 T. D. Noe, <a href="b002621.txt">Table of n, a(n) for n=0..1000</a>
%H A002621 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A002621 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A002621 P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               Sequences realized by oligomorphic permutation groups</a>, J. Integ. 
               Seqs. Vol. 3 (2000), #00.1.5.
%H A002621 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=199">
               Encyclopedia of Combinatorial Structures 199</a>
%H A002621 Thomas Wieder, The number of certain k-combinations of an n-set, <a href="http:/
               /www.math.nthu.edu.tw/~amen/">Applied Mathematics Electronic Notes</
               a>, vol. 8 (2008).
%p A002621 A002621 := proc(n) local s,x ; s := taylor(1/(1-x)^2,x=0,n+1) ; s := 
               taylor(s/(1-x^2),x=0,n+1) ; s := taylor(s/(1-x^3),x=0,n+1) ; s := 
               taylor(s/(1-x^4),x=0,n+1) ; coeftayl(s,x=0,n) ; end: for n from 0 
               to 80 do printf("%d, ",A002621(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jun 06 2007
%p A002621 A002621:=-1/(z**2+1)/(z**2+z+1)/(z+1)**2/(z-1)**5; [S. Plouffe in his 
               1992 dissertation.]
%p A002621 with(combstruct):ZL:=[st, {st=Prod(left, right), left=Set(U, card=r+2), 
               right=Set(U, card<r), U=Sequence(Z, card>=1)}, unlabeled]: subs(r=2, 
               stack): seq(count(subs(r=2, ZL), size=m), m=4..51) ; - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Feb 07 2008
%t A002621 CoefficientList[Series[1/((1-x)^2*(1-x^2)*(1-x^3)*(1-x^4)),{x,0,60}],
               x] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jun 
               10 2007
%Y A002621 Partial sums of A001400.
%Y A002621 Sequence in context: A011909 A065962 A049703 this_sequence A033500 A003318 
               A035300
%Y A002621 Adjacent sequences: A002618 A002619 A002620 this_sequence A002622 A002623 
               A002624
%K A002621 nonn,easy
%O A002621 0,2
%A A002621 N. J. A. Sloane (njas(AT)research.att.com).
%E A002621 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Stefan 
               Steinerberger (stefan.steinerberger(AT)gmail.com), Jun 06 2007

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