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A320547
Number of partitions of n into parts of exactly five sorts which are introduced in ascending order such that sorts of adjacent parts are different.
3
1, 11, 77, 438, 2216, 10423, 46732, 202826, 860599, 3593651, 14835058, 60735635, 247155920, 1001321100, 4043485479, 16288776186, 65500040622, 263035896496, 1055252507399, 4230340498375, 16949360224358, 67881450386237, 271777857121332, 1087867654290457
OFFSET
5,2
LINKS
FORMULA
a(n) ~ 4^(n-1) / (4! * QPochhammer[1/4]). - 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))(5):
seq(a(n), n=5..40);
MATHEMATICA
b[n_, i_, k_] := b[n, i, k] = If[n == 0 || i == 1, k^(n - 1), b[n, i - 1, k] + If[i > n, 0, k b[n - i, i, k]]];
A[n_, k_] := If[n == 0, 1, If[k < 2, k, k b[n, n, k - 1]]];
a[n_] := With[{k = 5}, Sum[A[n, k - i] (-1)^i/(i! (k - i)!), {i, 0, k}]];
a /@ Range[5, 40] (* Jean-François Alcover, Dec 08 2020, after Alois P. Heinz *)
CROSSREFS
Column k=5 of A262495.
Cf. A258460.
Sequence in context: A023010 A303103 A258459 * A022639 A000589 A211830
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 15 2018
STATUS
approved