Search: id:A001982
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%I A001982 M3441 N1396
%S A001982 1,4,12,31,71,147,285,519,902,1502,2417,3768,5722,8481,12310,17528,
%T A001982 24537,33814,45949,61629,81688,107089,138979,178669,227703,287828,
%U A001982 361075,449731,556423,684089,836078,1016110,1228391,1477573,1768875
%N A001982 Number of partitions of 4n-1 into n nonnegative integers each no greater 
               than 8.
%C A001982 In Cayley's terminology, this is the number of literal terms of degree 
               n and of weight 4n-1 involving the letters a, b, c, d, e, f, g, h, 
               i, having weights 0, 1, 2, 3, 4, 5, 6, 7, 8 respectively. - Herman 
               Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
%D A001982 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001982 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001982 A. Cayley, Numerical tables supplementary to second memoir on quantics, 
               Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, 
               London, 1889-1897, Vol. 2, p. 276-281.
%H A001982 A. Cayley, <a href="http://quod.lib.umich.edu/cgi/t/text/pageviewer-idx?c=umhistmath;
               cc=umhistmath;q1=second%20memoir%20on%20quantics;rgn=full%20text;
               cite1=cayley;cite1restrict=author;idno=ABS3153.0002.001;didno=ABS3153.0002.001;
               view=pdf;seq=00000289">Numerical tables supplementary to second memoir 
               on quantics</a>, Collected Mathematical Papers. Vols. 1-13, Cambridge 
               Univ. Press, London, 1889-1897, Vol. 2, p. 276-281.
%F A001982 Coefficient of x^w*z^n in the expansion of 1/((1-z)(1-xz)(1-x^2z)(1-x^3z)(1-x^4z)(1-x^5z)(1-x^6z)(1-x^7z)(1-x\
               ^8z)), where w=4n-1. - Herman Jamke (hermanjamke(AT)fastmail.fm), 
               Feb 17 2008
%o A001982 (PARI) f=1/((1-z)*(1-x*z)*(1-x^2*z)*(1-x^3*z)*(1-x^4*z)*(1-x^5*z)*(1-x^6*z)*(1-x^7*z)*(1-x^8*z)); 
               n=400; p=subst(subst(f,x,x+x*O(x^n)),z,z+z*O(z^n)); for(d=1,60,w=4*d-1;
               print1(polcoeff(polcoeff(p,w),d)",")) - Herman Jamke (hermanjamke(AT)fastmail.fm), 
               Feb 17 2008
%Y A001982 Cf. A001981.
%Y A001982 Sequence in context: A005289 A037255 A027658 this_sequence A129707 A133546 
               A171844
%Y A001982 Adjacent sequences: A001979 A001980 A001981 this_sequence A001983 A001984 
               A001985
%K A001982 nonn
%O A001982 0,2
%A A001982 N. J. A. Sloane (njas(AT)research.att.com).
%E A001982 Better definition and more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), 
               Feb 17 2008

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