A369770 a(n) is the maximal coefficient in the expansion of Product_{k=1..n} (1+k*x)^k.

1, 1, 8, 387, 192832, 1348952000, 142641794707200, 271057611231886800384, 10679112895658933205816311808, 9866210328276596971591655994333069312, 238373589086269734817383263830485997977600000000, 166142193793387680126634957823414405189312889036472320000000

Offset: 0

Author

Joerg Arndt, Jan 31 2024

Keywords

• nonn

Crossrefs

Cf. A065048 (maximal coefficient in Product_{k=1..n} (1+k*x) ).

Programs

Maple

b:= proc(n) b(n):= `if`(n=0, 1, expand(b(n-1)*(1+n*x)^n)) end:
a:= n-> max(coeffs(b(n))):
seq(a(n), n=0..11);  # Alois P. Heinz, Jan 31 2024

PARI

a(n)=vecmax(Vec(prod(k=1,n,(1+k*x)^k)));
vector(20,n,a(n-1))

Python

from collections import Counter
from math import comb
def A369770(n):
    c = {0:1}
    for k in range(1,n+1):
        d = Counter(c)
        for j in c:
            a = c[j]
            for i in range(1,k+1):
                d[j+i] += comb(k,i)*k**i*a
        c = d
    return max(c.values()) # Chai Wah Wu, Jan 31 2024