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

%I A369770 #12 Jan 31 2024 19:13:20
%S A369770 1,1,8,387,192832,1348952000,142641794707200,271057611231886800384,
%T A369770 10679112895658933205816311808,9866210328276596971591655994333069312,
%U A369770 238373589086269734817383263830485997977600000000,166142193793387680126634957823414405189312889036472320000000
%N A369770 a(n) is the maximal coefficient in the expansion of Product_{k=1..n} (1+k*x)^k.
%p A369770 b:= proc(n) b(n):= `if`(n=0, 1, expand(b(n-1)*(1+n*x)^n)) end:
%p A369770 a:= n-> max(coeffs(b(n))):
%p A369770 seq(a(n), n=0..11);  # _Alois P. Heinz_, Jan 31 2024
%o A369770 (PARI) a(n)=vecmax(Vec(prod(k=1,n,(1+k*x)^k)));
%o A369770 vector(20,n,a(n-1))
%o A369770 (Python)
%o A369770 from collections import Counter
%o A369770 from math import comb
%o A369770 def A369770(n):
%o A369770     c = {0:1}
%o A369770     for k in range(1,n+1):
%o A369770         d = Counter(c)
%o A369770         for j in c:
%o A369770             a = c[j]
%o A369770             for i in range(1,k+1):
%o A369770                 d[j+i] += comb(k,i)*k**i*a
%o A369770         c = d
%o A369770     return max(c.values()) # _Chai Wah Wu_, Jan 31 2024
%Y A369770 Cf. A065048 (maximal coefficient in Product_{k=1..n} (1+k*x) ).
%K A369770 nonn
%O A369770 0,3
%A A369770 _Joerg Arndt_, Jan 31 2024