Apropos my last, EIS gives for A000701, Name: One half of number of non-self-conjugate partitions; also half of number of asymmetric Ferrers graphs with n nodes. Comments: Also number of cycle types of odd permutations. Also number of partitions of n with an odd number of even parts. There is no restriction on the odd parts. but no generating function. This is no problem, since A000701 = (A000041-A000700)/2, but in case Neil wants to add some, here are the expressions I gave last time plus a couple more. oo ==== \ n + 2 2 3 4 5 6 7 8
A000701(n) q = q + q + 2 q + 3 q + 5 q + 7 q + 10 q / ==== n = 0
9 10 11 12 13 14 15 + 14 q + 20 q + 27 q + 37 q + 49 q + 66 q + 86 q + . . . oo ==== 2 \ 2 n > (- q ) / oo ==== ==== 2 (2 n - 1) n = 1 \ q = - ----------------------------- = (- q; q) > --------------- oo n (3 n - 1) oo / 2 2 ==== ----------- ==== (q ; q ) \ n 2 n = 1 2 n - 1 > (- 1) q / ==== n = - oo 1 1 1 2 -------- - ---------- -------- - (- q; q ) (q; q) (q; - q) (q; q) oo oo oo oo = ----------------------- = ---------------------- 2 2 oo 2 ==== k \ 1 1 q = > (------- - ---------) --- , / 2 2 2 2 ==== (q; q) (q ; q ) k = 0 k k n-1 where "q-pochhammer" notation (a;q)_n := prod 1-a*q^k . k=0 The this last sum and the ratio of sums are perhaps most efficient, but among the seemingly endless variations I can't find a simple monomial product. --rwg GLISSADE <-> SLIDAGES