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A335651 a(n) is the sum, over all overpartitions of n, of the non-overlined parts. 3
1, 5, 14, 35, 74, 150, 280, 505, 875, 1470, 2402, 3850, 6034, 9300, 14120, 21131, 31220, 45619, 65930, 94374, 133892, 188350, 262904, 364350, 501459, 685762, 932200, 1259944, 1693750, 2265380, 3015152, 3994585, 5268988, 6920700, 9053748, 11798873, 15319610, 19820738, 25557560 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
K. Bringmann, J. Lovejoy, and R. Osburn, Rank and crank moments for overpartitions, Journal of Number Theory, 129 (2009), 1758-1772.
FORMULA
G.f.: (Product_{k>=1} (1+q^k)/(1-q^k)) * Sum_{n>=1} n*q^n/(1-q^n).
a(n) = A235793(n) - A335666(n). - Omar E. Pol, Jun 17 2020
EXAMPLE
The 8 overpartitions of 3 are [3], [3'], [2,1], [2,1'], [2',1], [2',1'], [1,1,1], [1',1,1], and so a(3) = 14.
PROG
(PARI) my(N=44, q='q+O('q^N)); Vec( prod(k=1, N, (1+q^k)/(1-q^k)) * sum(k=1, N, k*q^k/(1-q^k)) ) \\ Joerg Arndt, Jun 18 2020
CROSSREFS
Cf. A305102 (number of non-overlined parts).
Sequence in context: A101015 A076858 A001215 * A066767 A227200 A027974
KEYWORD
nonn
AUTHOR
Jeremy Lovejoy, Jun 17 2020
STATUS
approved

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Last modified April 18 22:18 EDT 2024. Contains 371782 sequences. (Running on oeis4.)