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A003283
Denominators of coefficients of Green function for cubic lattice.
(Formerly M2116)
1
1, 2, 20, 70, 112, 352, 1232, 22880, 183040, 1244672, 30098432, 72352, 2472371200, 115763200, 441223168, 6838959104, 61568122880, 745298329600, 28321336524800, 1103041527808, 573581594460160, 4275790067793920, 49961677422592
OFFSET
0,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
G. S. Joyce, The simple cubic lattice Green function, Phil. Trans. Roy. Soc., 273 (1972), 583-610.
FORMULA
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 denominator of C(n). - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
PROG
(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(denominator(C[n+3])", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
CROSSREFS
Cf. A003282.
Sequence in context: A216609 A226394 A287485 * A259110 A135188 A161007
KEYWORD
nonn,easy,frac
EXTENSIONS
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
STATUS
approved