A003280 Numerators of coefficients of Green function for cubic lattice. (Formerly M4664)

1, 9, 175, 2025, 102235, 1356047, 37160123, 6771931925, 772428184055, 189690563847015, 105217453376898775, 1548913291275244825, 2112565685454158552975, 1658173107161491979625

Offset

0,2

References

G. S. Joyce, The simple cubic lattice Green function, Phil. Trans. Roy. Soc., 273 (1972), 583-610.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008, Table of n, a(n) for n = 0..23

Formula

Let {B0(n)} be the sequence of rational numbers defined by the recurrence: 16*n*(n+1)*(2n+1)*B0(n+1) - n*(60*n^2+9)*B0(n) + 3*(2n-1)^3*B0(n-1) + (n-1)*(2n-1)*(2n-3)*B0*(n-2) = 0 for n >= 1 with B0(0) = 1 and B0(1) = 9/32. Then a(n) is the numerator of B0(n). - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008

Prog

(PARI) B0=vector(100); B0[3]=1; B0[4]=9/32; print1("1, 9, "); for(n=2, 30, B0[n+3]=((n-1)*(60*(n-1)^2+9)*B0[n+2]-3*(2*n-3)^3*B0[n+1]-(n-2)*(2*n-3)*(2*n-5)*B0[n])/(16*(n-1)*n*(2*n-1)); print1(numerator(B0[n+3])", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008

Crossrefs

Sequence in context: A336728 A305465 A027956 * A201536 A141359 A141363

Adjacent sequences: A003277 A003278 A003279 * A003281 A003282 A003283

Keyword

nonn,easy,frac

Author

N. J. A. Sloane

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008

Status

approved