A178882 - OEIS

A178882

Irregular triangle T(n,k) = n!* A036040(n,k), read by rows, 1 <= k <= A000041(n).

1, 1, 2, 2, 6, 18, 6, 24, 96, 72, 144, 24, 120, 600, 1200, 1200, 1800, 1200, 120, 720, 4320, 10800, 7200, 10800, 43200, 10800, 14400, 32400, 10800, 720, 5040, 35280, 105840, 176400, 105840, 529200, 352800, 529200, 176400, 1058400, 529200, 176400, 529200, 105840, 5040

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

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

Triangle begins:

0 | 1;

1 | 1;

2 | 2, 2;

3 | 6, 18, 6;

4 | 24, 96, 72, 144, 24;

5 | 120, 600, 1200, 1200, 1800, 1200, 120;

6 | 720, 4320, 10800, 7200, 10800, 43200, 10800, 14400, 32400, 10800, 720;

...

For row n = 4 the calculations are (1 4 3 6 1) times (24 24 24 24 24 ) yielding (24 96 72 144 24) which sums to A137341(4) = 360.

PROG

(PARI)

C(sig)={my(S=Set(sig)); vecsum(sig)!^2/prod(k=1, #sig, sig[k]!)/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), A000110, A036036, A036040, A053529, A137341 (row sums), A036040, A178801.

Sequence in context: A006249 A216971 A019575 * A186195 A256215 A253284

Adjacent sequences: A178879 A178880 A178881 * A178883 A178884 A178885

KEYWORD

easy,nonn,tabf

AUTHOR

Alford Arnold, Jun 23 2010

EXTENSIONS

a(0)=1 prepended and a(36) onwards from Andrew Howroyd, Oct 02 2025

STATUS

approved