A321897 - OEIS

A321897

Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of p(v) in h(u) * Product_i u_i!, where H is Heinz number, h is homogeneous symmetric functions, and p is power sum symmetric functions.

1, 1, 1, 1, 0, 1, 2, 3, 1, 0, 1, 1, 6, 3, 8, 6, 1, 0, 0, 1, 0, 1, 0, 2, 1, 0, 0, 2, 3, 1, 24, 30, 20, 15, 20, 10, 1, 0, 0, 0, 1, 1, 120, 90, 144, 40, 15, 90, 120, 45, 40, 15, 1, 0, 6, 0, 3, 8, 6, 1, 0, 0, 2, 3, 2, 4, 1, 0, 0, 0, 0, 1, 720, 840, 504, 420, 630

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

OFFSET

1,7

COMMENTS

Row n has length A000041(A056239(n)).

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

LINKS

Table of n, a(n) for n=1..77.

Wikipedia, Symmetric polynomial

EXAMPLE

Triangle begins:

1 1

0 1

2 3 1

0 1 1

6 3 8 6 1

0 0 1

0 1 0 2 1

0 0 2 3 1

24 30 20 15 20 10 1

0 0 0 1 1

120 90 144 40 15 90 120 45 40 15 1

0 6 0 3 8 6 1

0 0 2 3 2 4 1

0 0 0 0 1

720 840 504 420 630 504 210 280 105 210 420 105 70 21 1

0 0 0 1 0 2 1

For example, row 14 gives: 12h(41) = 6p(41) + 3p(221) + 8p(311) + 6p(2111) + p(11111).

CROSSREFS

Row sums are A321898.

Cf. A005651, A008480, A056239, A124794, A124795, A319193, A321742-A321765, A321896.

Sequence in context: A079343 A004566 A321896 * A050074 A346688 A278313

Adjacent sequences: A321894 A321895 A321896 * A321898 A321899 A321900

KEYWORD

nonn,tabf

AUTHOR

Gus Wiseman, Nov 20 2018

STATUS

approved