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A320735
Number of partitions of n with four sorts of part 1 which are introduced in ascending order.
4
1, 1, 3, 7, 20, 62, 217, 803, 3092, 12128, 48047, 191266, 763249, 3049383, 12190360, 48747140, 194960047, 779783252, 3119019290, 12475849884, 49902945245, 199610872683, 798441674561, 3193763066392, 12775045002551, 51100165484967, 204400632890492
OFFSET
0,3
LINKS
MAPLE
b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
Stirling2(n, j), j=0..4), 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, 4}], 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=4 of A292745.
Sequence in context: A357792 A361625 A056783 * A176697 A320736 A320737
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 20 2018
STATUS
approved