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A320734
Number of partitions of n with three sorts of part 1 which are introduced in ascending order.
4
1, 1, 3, 7, 19, 52, 151, 442, 1314, 3921, 11737, 35171, 105464, 316318, 948863, 2846461, 8539221, 25617443, 76852054, 230555794, 691666924, 2075000173, 6224999772, 18674998357, 56024993883, 168074980137, 504224938548, 1512674813304, 4538024437036
OFFSET
0,3
LINKS
MAPLE
b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
Stirling2(n, j), j=0..3), add(b(n-i*j, i-1), j=0..n/i))
end:
a:= n-> b(n$2):
seq(a(n), n=0..40);
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, 3}], Sum[b[n - i j, i - 1], {j, 0, n/i}]];
a[n_] := b[n, n];
a /@ Range[0, 40] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)
CROSSREFS
Column k=3 of A292745.
Sequence in context: A135052 A198305 A146597 * A259812 A115254 A222324
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 20 2018
STATUS
approved