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A003280 Numerators of coefficients of Green function for cubic lattice.
(Formerly M4664)
1
1, 9, 175, 2025, 102235, 1356047, 37160123, 6771931925, 772428184055, 189690563847015, 105217453376898775, 1548913291275244825, 2112565685454158552975, 1658173107161491979625 (list; graph; refs; listen; history; text; internal format)
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: 16n(n+1)(2n+1)B0(n+1)-n(60n^2+9)B0(n)+3(2n-1)^3B0(n-1)+(n-1)(2n-1)(2n-3)B0(n-2)=0 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

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Last modified December 8 17:01 EST 2021. Contains 349596 sequences. (Running on oeis4.)