A394291 - OEIS

A394291

Number of partitions of n such that the multiplicity m of the least part s is a part of the partition and m > s.

0, 0, 0, 1, 0, 2, 1, 4, 4, 8, 7, 17, 16, 28, 33, 52, 57, 90, 102, 149, 178, 244, 289, 400, 473, 624, 754, 979, 1171, 1510, 1804, 2284, 2745, 3426, 4102, 5100, 6081, 7472, 8925, 10890, 12949, 15722, 18648, 22489, 26651, 31952, 37742, 45100, 53126

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OFFSET

1,6

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..1000

FORMULA

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

EXAMPLE

a(10) counts these 8 partitions: 6211, 511111, 43111, 42211, 421111, 33211, 322111, 222211.

PROG

(PARI) my(N=50, q='q+O('q^N)); concat([0, 0, 0], Vec(sum(j=1, N, sum(k=j+1, N, q^((j+1)*k))/prod(k=j+1, N, 1-q^k))))

CROSSREFS

Cf. A096403, A240493.

Sequence in context: A345442 A060723 A300622 * A195691 A074763 A099932

Adjacent sequences: A394288 A394289 A394290 * A394292 A394293 A394294

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Mar 15 2026

STATUS

approved