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A292503
Number of partitions of n with n sorts of part 1 which are introduced in ascending order.
7
1, 1, 3, 7, 20, 63, 233, 966, 4454, 22404, 121616, 706362, 4361977, 28494493, 196087988, 1416515642, 10709058487, 84505818259, 694397612486, 5929368380664, 52513737017847, 481577858196052, 4565851595293151, 44692014464166068, 451058715629365617
OFFSET
0,3
LINKS
EXAMPLE
a(2) = 3: 2, 1a1a, 1a1b.
a(3) = 7: 3, 21a, 1a1a1a, 1a1a1b, 1a1b1a, 1a1b1b, 1a1b1c.
MAPLE
f:= (n, k)-> add(Stirling2(n, j), j=0..k):
b:= proc(n, i, k) option remember; `if`(n=0 or i<2,
f(n, k), add(b(n-i*j, i-1, k), j=0..n/i))
end:
a:= n-> b(n$3):
seq(a(n), n=0..30);
MATHEMATICA
f[n_, k_] := Sum[StirlingS2[n, j], {j, 0, k}];
b[n_, i_, k_] := b[n, i, k] = If[n == 0 || i < 2, f[n, k], Sum[b[n - i*j, i - 1, k], {j, 0, n/i}]];
a[n_] := b[n, n, n];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 17 2018, translated from Maple *)
CROSSREFS
Main diagonal of A292745.
Row sums of A292746.
Sequence in context: A320739 A320740 A320741 * A340357 A071688 A232687
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 17 2017
STATUS
approved