OFFSET
0,4
LINKS
T. D. Noe, Table of n, a(n) for n = 0..1000
Arnold Knopfmacher and Neville Robbins, Identities for the total number of parts in partitions of integers, Util. Math. 67 (2005), 9-18.
FORMULA
G.f.: A(q) = Sum_{n >= 1} n*q^(2*n-1)*(1+q)*(1+q^3)*...*(1+q^(2*n-3)).
From Peter Bala, Aug 20 2017: (Start)
Let F(q) = Product_{i >= 1} (1 + q^(2*i-1)). Then A(q) = Sum_{n >= 0} ( F(q) - Product_{i = 1..n} (1 + q^(2*i-1)) ).
It follows that the above sum A(q) satisfies -A(q-1) = 1 + q + 3*q^2 + 12*q^3 + 61*q^4 + ..., the g.f. for A158691, row-Fishburn matrices of size n. (End)
MATHEMATICA
CoefficientList[Series[Sum[n*q^(2n-1)*Product[1+q^k, {k, 1, 2n-3, 2}], {n, 1, 30}], {q, 0, 60}], q]
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Naohiro Nomoto, Feb 01 2002
EXTENSIONS
Edited by Dean Hickerson, Feb 11 2002
STATUS
approved