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A369770
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a(n) is the maximal coefficient in the expansion of Product_{k=1..n} (1+k*x)^k.
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1
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1, 1, 8, 387, 192832, 1348952000, 142641794707200, 271057611231886800384, 10679112895658933205816311808, 9866210328276596971591655994333069312, 238373589086269734817383263830485997977600000000, 166142193793387680126634957823414405189312889036472320000000
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OFFSET
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0,3
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LINKS
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MAPLE
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b:= proc(n) b(n):= `if`(n=0, 1, expand(b(n-1)*(1+n*x)^n)) end:
a:= n-> max(coeffs(b(n))):
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PROG
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(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
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
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CROSSREFS
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Cf. A065048 (maximal coefficient in Product_{k=1..n} (1+k*x) ).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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