A394188 Number of partitions of n such that (number of distinct parts) <= minimal multiplicity of the parts.

1, 1, 2, 2, 3, 2, 5, 3, 7, 6, 10, 8, 16, 11, 20, 17, 26, 20, 36, 26, 43, 37, 54, 44, 73, 56, 85, 80, 106, 93, 140, 118, 162, 161, 198, 184, 257, 228, 289, 301, 350, 337, 440, 408, 498, 521, 585, 582, 734, 690, 812, 867, 962, 962, 1172, 1135, 1311, 1396, 1523, 1550, 1870, 1809, 2055

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: Sum_{j>=0} [z^j] Product_{k>=1} (1 + z*q^(j*k)/(1-q^k)).

Example

a(8) = 7 counts these partitions: 8, 44, 3311, 2222, 22211, 221111, 11111111.

Prog

(PARI) my(N=70, q='q+O('q^N)); Vec(sum(j=0, N, polcoef(prod(k=1, N, 1+z*q^(j*k)/(1-q^k)), j, z)))

Crossrefs

Cf. A239966, A240306, A394189.

Sequence in context: A281121 A382129 A378744 * A220949 A029656 A121306

Adjacent sequences: A394185 A394186 A394187 * A394189 A394190 A394191

Keyword

nonn

Author

Seiichi Manyama, Mar 12 2026

Status

approved