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A320692
Number of partitions of n with up to five distinct kinds of 1.
2
1, 5, 11, 16, 22, 33, 49, 70, 98, 135, 184, 248, 330, 436, 572, 743, 959, 1232, 1572, 1994, 2518, 3165, 3961, 4936, 6125, 7575, 9338, 11469, 14041, 17142, 20867, 25331, 30671, 37042, 44629, 53647, 64342, 77007, 91977, 109632, 130426, 154884, 183596, 217250
OFFSET
0,2
LINKS
FORMULA
a(n) ~ Pi * 2^(5/2) * exp(Pi*sqrt(2*n/3)) / (3 * n^(3/2)). - Vaclav Kotesovec, Oct 24 2018
G.f.: (1 + x)^5 * Product_{k>=2} 1 / (1 - x^k). - Ilya Gutkovskiy, Apr 24 2021
MAPLE
b:= proc(n, i) option remember; `if`(n=0 or i=1,
binomial(5, n), `if`(i>n, 0, b(n-i, i))+b(n, i-1))
end:
a:= n-> b(n$2):
seq(a(n), n=0..60);
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0 || i == 1, Binomial[5, n], If[i > n, 0, b[n - i, i]] + b[n, i - 1]];
a[n_] := b[n, n];
a /@ Range[0, 60] (* Jean-François Alcover, Dec 14 2020 *)
CROSSREFS
Column k=5 of A292622.
Sequence in context: A314169 A299911 A314170 * A314171 A314172 A314173
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 19 2018
STATUS
approved