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A320551 Number of partitions of n into parts of exactly nine sorts which are introduced in ascending order such that sorts of adjacent parts are different. 3
1, 37, 788, 12705, 172520, 2084836, 23169639, 241881526, 2406802476, 23064505722, 214505275666, 1947297442708, 17332491414655, 151788374232332, 1311496639251360, 11205023121317869, 94832831557101194, 796244028802170279, 6640545376656272033 (list; graph; refs; listen; history; text; internal format)
OFFSET
9,2
LINKS
FORMULA
a(n) ~ 8^(n-1) / (8! * QPochhammer[1/8]). - Vaclav Kotesovec, Oct 25 2018
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0 or i=1, k^(n-1),
b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k)))
end:
A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, k*b(n$2, k-1))):
a:= n-> (k-> add(A(n, k-i)*(-1)^i/(i!*(k-i)!), i=0..k))(9):
seq(a(n), n=9..40);
CROSSREFS
Column k=9 of A262495.
Cf. A258464.
Sequence in context: A220684 A225971 A258463 * A211834 A216439 A333065
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 15 2018
STATUS
approved

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Last modified July 19 11:53 EDT 2024. Contains 374394 sequences. (Running on oeis4.)