* Bill Gosper <billgosper@gmail.com> [Oct 08. 2012 08:02]:
(For R-R, special-case a:=q)
[...]
[ inf 2 ] [ ==== n n ] [ \ a q ] [ 0 a > -------------- ] inf [ / qpoch(q, q, n) ] /===\ [ ==== ] | | [ 0 a ] [ n = 0 ] (d44) | | [ ] = [ ] | | [ k ] [ inf 2 ] k = 0 [ q 1 ] [ ==== n n - n ] [ \ a q ] [ 0 > -------------- ] [ / qpoch(q, q, n) ] [ ==== ] [ n = 0 ]
[...]
I toyed around a bit (note my start k=1 of the product): [ inf 2 ] [ ==== n ] [ \ q ] [ 0 > -------------- ] (UR = H(q) = A003106) inf [ / qpoch(q, q, n) ] /===\ [ ==== ] | | [ 0 1 ] [ n = 0 ] (dxx) | | [ ] = [ ] | | [ k ] [ inf 2 ] k = 1 [ q 1 ] [ ==== n + n ] [ \ q ] [ 0 > -------------- ] (LR= G(q) = A003114) [ / qpoch(q, q, n) ] [ ==== ] [ n = 0 ] I.e., R-R proper. I am much tempted to put that into both A003106 and A003114 (obviously with attribution to RWG). OK, Neil ? [ inf 2 ] [ ==== n - n ] [ \ q ] [ 0 q > -------------- ] (UR=A006141) inf [ / qpoch(q, q, n) ] /===\ [ ==== ] | | [ 0 q ] [ n = 0 ] (dxx) | | [ ] = [ ] | | [ k ] [ inf 2 ] k = 1 [ q 1 ] [ ==== n ] [ \ q ] [ 0 > -------------- ] (LR= H(q) = A003106) [ / qpoch(q, q, n) ] [ ==== ] [ n = 0 ] inf /===\ | | [ 0 q^n ] [ 0 D(q) ] (D=A000009) (dxx) | | [ ] = [ ] | | [ k ] [ 0 D(q) ] (D=A000009) k = 1 [ 1+q 1 ] inf /===\ | | [ 0 -q^n ] [ 0 E(q) ] (E=A010815 = 1/A000041) (dxx) | | [ ] = [ ] | | [ k ] [ 0 E(q) ] (E=A010815 = 1/A000041) k = 1 [1-q 1 ] ASCII for president!