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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..250

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

Cf. A292462, A292463, A292507.

Main diagonal of A292745.

Row sums of A292746.

Sequence in context: A320739 A320740 A320741 * A340357 A071688 A232687

Adjacent sequences: A292500 A292501 A292502 * A292504 A292505 A292506

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 17 2017

STATUS

approved

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Last modified January 30 17:11 EST 2023. Contains 359945 sequences. (Running on oeis4.)