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A320549
Number of partitions of n into parts of exactly seven sorts which are introduced in ascending order such that sorts of adjacent parts are different.
3
1, 22, 289, 2957, 26073, 208516, 1558219, 11087757, 76079369, 507834036, 3318628468, 21330628088, 135325211035, 849659803048, 5290544985029, 32722489543068, 201296535411532, 1232850239281547, 7523511821702402, 45777353201698899, 277862479922939524
OFFSET
7,2
LINKS
FORMULA
a(n) ~ 6^(n-1) / (6! * QPochhammer[1/6]). - 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))(7):
seq(a(n), n=7..40);
CROSSREFS
Column k=7 of A262495.
Cf. A258462.
Sequence in context: A121792 A020922 A258461 * A211832 A211559 A333063
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 15 2018
STATUS
approved