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%I M4360 #22 Oct 22 2023 02:25:58
%S 1,1,7,19,25,67,205,3389,24469,151805,3378595,7529,239951407,10532699,
%T 37801901,553870985,4729453873,54466083977,1974303293437,73525821439,
%U 36638106109621,262239579597193,2947415049407,90871116596785
%N Numerators of coefficients of Green function for cubic lattice.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H G. S. Joyce, <a href="http://www.jstor.org/stable/74037">The simple cubic lattice Green function</a>, Phil. Trans. Roy. Soc., 273 (1972), 583-610.
%F Let {C(n)} be the sequence of rational numbers defined by the recurrence: 8*(n+1)*(2n+1)*(2n+3)*C(n+1) - 6*(2n+1)*(5n^2+5n+2)*C(n) + 24*n^3*C(n-1) + 2*n*(n-1)*(2n-1)*C(n-2) = 0 for n >= 0 with C(0) = 1 and C(n) = 0 if n < 0. Then a(n) is the numerator of C(n). - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
%o (PARI) C=vector(100);C[3]=1;print1(C[3]",");for(n=1,30,C[n+3]=(6*(2*n-1)*(5*n^2-5*n+2)*C[n+2]-24*(n-1)^3*C[n+1]-2*(n-1)*(n-2)*(2*n-3)*C[n])/(8*n*(2*n-1)*(2*n+1));print1(numerator(C[n+3])",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
%Y Cf. A003283.
%K nonn,easy,frac
%O 0,3
%A _N. J. A. Sloane_
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
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