A182779 Irregular triangle T(n,k) = A049019(n,k) * A118851(n,k), read by rows, 1 <= k <= A000041(n).

1, 1, 2, 2, 3, 12, 6, 4, 24, 24, 72, 24, 5, 40, 120, 180, 360, 480, 120, 6, 60, 240, 180, 360, 2160, 720, 1440, 4320, 3600, 720, 7, 84, 420, 840, 630, 5040, 3780, 7560, 3360, 30240, 20160, 12600, 50400, 30240, 5040, 8, 112, 672, 1680, 1120, 1008, 10080, 20160, 20160

Offset

0,3

Comments

Rows have A000041(n) entries, with partitions in Abramowitz and Stegun order (A036036).

Links

Andrew Howroyd, Table of n, a(n) for n = 0..2713 (rows 0..20)

Example

For n = 3 the values are (3,12,6) = (1,6,6)*(3,2,1).
Table starts:
1;
1;
2, 2;
3, 12, 6;
4, (24, 24), 72, 24;
5, (40, 120), (180, 360), 480, 120;
6, (60, 240, 180), (360, 2160, 720), (1440, 4320), 3600, 720;
7, (84, 420, 840), (630, 5040, 3780, 7560), (3360, 30240, 20160), (12600, 50400), 30240, 5040;

Prog

(PARI)
C(sig)={my(S=Set(sig)); vecsum(sig)!*(#sig)!/prod(k=1, #sig, (sig[k]-1)!)/prod(k=1, #S, (#select(t->t==S[k], sig))!)}
Row(n)={apply(C, [Vecrev(p) | p<-partitions(n)])}
{ for(n=0, 7, print(Row(n))) } \\ Andrew Howroyd, Oct 02 2025

Crossrefs

Cf. A000041 (row lengths), A006153 (row sums), A036036, A049019, A118851.

Sequence in context: A178343 A156136 A134243 * A199673 A377660 A375218

Adjacent sequences: A182776 A182777 A182778 * A182780 A182781 A182782

Keyword

nonn,tabf

Author

Alford Arnold, Dec 01 2010

Extensions

a(0) = 1 prepended by Peter Luschny, May 31 2020

a(45) onwards from Andrew Howroyd, Oct 02 2025

Status

approved