A369767 - OEIS

A369767

Maximal coefficient of Product_{i=1..n} Sum_{j=0..n} x^(i*j).

1, 1, 2, 6, 31, 231, 2347, 29638, 449693, 7976253, 162204059, 3722558272, 95221978299, 2687309507102, 82967647793153, 2782190523572392, 100715040802229833, 3914979746952224303, 162662679830709439637, 7194483479557973730982, 337519906320930133470189

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

MAPLE

a:= n-> max(coeffs(expand(mul(add(x^(i*j), j=0..n), i=1..n)))):

seq(a(n), n=0..20); # Alois P. Heinz, Jan 31 2024

MATHEMATICA

Table[Max[CoefficientList[Product[Sum[x^(i j), {j, 0, n}], {i, 1, n}], x]], {n, 0, 20}]

PROG

(PARI) a(n) = vecmax(Vec(prod(i=1, n, sum(j=0, n, x^(i*j))))); \\ Michel Marcus, Jan 31 2024

(Python)

from collections import Counter

def A369767(n):

c = {j:1 for j in range(n+1)}

for i in range(2, n+1):

d = Counter()

for k in c:

for j in range(0, i*n+1, i):

d[j+k] += c[k]

c = d

return max(c.values()) # Chai Wah Wu, Jan 31 2024

CROSSREFS

Cf. A000041, A025591, A077047.

Sequence in context: A275558 A094639 A113719 * A018225 A217143 A075845

Adjacent sequences: A369764 A369765 A369766 * A369768 A369769 A369770

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 31 2024

STATUS

approved