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%I M2545 N1006 #26 Jun 25 2023 02:48:39
%S 0,1,3,6,11,19,32,48,71,101,141,188,249,322,414,518,645,791,966,1160,
%T 1389,1645,1943,2268,2642,3053,3521,4026,4596,5214,5907,6648,7473,
%U 8359,9339,10380,11526,12747,14085,15498,17039,18671,20444,22308,24326,26452,28746
%N Number of partitions of floor(5n/2)-1 into n nonnegative integers each no more than 5.
%C In Cayley's terminology, this is the number of literal terms of degree n and of weight floor(5n/2)-1 involving the letters a, b, c, d, e, f, having weights 0, 1, 2, 3, 4, 5 respectively. - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
%D A. Cayley, Numerical tables supplementary to second memoir on quantics, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 2, pp. 276-281.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Alois P. Heinz, <a href="/A001976/b001976.txt">Table of n, a(n) for n = 0..1000</a>
%H 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, pp. 276-281.
%H A. Cayley, <a href="/A001971/a001971.pdf">Numerical tables supplementary to second memoir on quantics</a>, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 2, pp. 276-281. [Annotated scanned copy]
%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1, 0, 1, -2, 2, -2, 2, -2, 0, 2, -2, 2, -2, 2, -1, 0, 1, -2, 1).
%F 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)), where w=floor(5n/2)-1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
%F G.f.: -(x^12 +x^11 +x^10 +2*x^9 +2*x^8 +4*x^7 +x^6 +4*x^5 +2*x^4 +2*x^3 +x^2 +x+1)*x / ((x^4+1) *(x^2+x+1) *(x^2-x+1) *(x^2+1)^2 *(x+1)^3 *(x-1)^5). - _Alois P. Heinz_, Jul 25 2015
%o (PARI) f=1/((1-z)*(1-x*z)*(1-x^2*z)*(1-x^3*z)*(1-x^4*z)*(1-x^5*z)); n=350; p=subst(subst(f,x,x+x*O(x^n)),z,z+z*O(z^n)); for(d=0,60,w=floor(5*d/2)-1;print1(polcoeff(polcoeff(p,w),d)",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
%Y Cf. A001975.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
%E Better definition and more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
%E a(0)=0 inserted by _Alois P. Heinz_, Jul 25 2015
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