A221584 A sum over partitions (q=20), see first comment.

1, 19, 399, 7980, 159980, 3199581, 63999600, 1279991601, 25599991620, 511999832020, 10239999832020, 204799996632420, 4095999996640419, 81919999932640800, 1638399999932648400, 32767999998652808799, 655359999998652816380, 13107199999973052976380

Offset: 0

Author

Joerg Arndt, Jan 20 2013

Keywords

• nonn

Comments

Set q=20 and f(m)=q^(m-1)*(q-1), then a(n) is the sum over all partitions P of n over all products Product_{k=1..L} f(m_k) where L is the number of different parts in the partition P=[p_1^m_1, p_2^m_2, ..., p_L^m_L].

Setting q to a prime power gives the sequence "Number of conjugacy classes in GL(n,q)":

q=3: A006952, q=4: A049314, q=5: A049315, q=7: A049316, q=8: A182603,

q=9: A182604, q=11: A182605, q=13: A182606, q=16: A182607, q=17: A182608,

q=19: A182609, q=23: A182610, q=25: A182611, q=27: A182612.

Sequences where q is not a prime power:

q=6: A221578, q=10: A221579, q=12: A221580,

q=14: A221581, q=15: A221582, q=18: A221583, q=20: A221584.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100

Programs

PARI

N=66; x='x+O('x^N);
gf=prod(n=1,N, (1-x^n)/(1-20*x^n)  );
v=Vec(gf)