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A347867
Number of partitions of n such that 3*(greatest part) >= (number of parts).
2
1, 2, 3, 4, 6, 10, 14, 20, 27, 38, 51, 70, 92, 123, 162, 212, 274, 355, 453, 579, 733, 928, 1165, 1463, 1822, 2269, 2808, 3470, 4266, 5241, 6407, 7823, 9514, 11554, 13983, 16900, 20359, 24494, 29386, 35205, 42069, 50206, 59773, 71069, 84322, 99913, 118157, 139556, 164528, 193734
OFFSET
1,2
COMMENTS
Also, the number of partitions of n such that (greatest part) <= 3*(number of parts).
FORMULA
G.f.: Sum_{k>=1} x^k * Product_{j=1..k} (1-x^(3*k+j-1))/(1-x^j).
PROG
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, x^k*prod(j=1, k, (1-x^(3*k+j-1))/(1-x^j))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 25 2022
STATUS
approved