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A369770
a(n) is the maximal coefficient in the expansion of Product_{k=1..n} (1+k*x)^k.
1
1, 1, 8, 387, 192832, 1348952000, 142641794707200, 271057611231886800384, 10679112895658933205816311808, 9866210328276596971591655994333069312, 238373589086269734817383263830485997977600000000, 166142193793387680126634957823414405189312889036472320000000
OFFSET
0,3
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
PROG
(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
CROSSREFS
Cf. A065048 (maximal coefficient in Product_{k=1..n} (1+k*x) ).
Sequence in context: A085806 A042115 A159515 * A220799 A220785 A203368
KEYWORD
nonn
AUTHOR
Joerg Arndt, Jan 31 2024
STATUS
approved