A321892 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of f(v) in s(u), where H is Heinz number, f is forgotten symmetric functions, and s is Schur functions.

1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 2, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 4, 0, 0, 0, 1, 0, 2, 5

Offset

1,12

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..67.

Wikipedia, Symmetric polynomial

Example

Triangle begins:
   1
   1
   0   1
   1   1
   0   0   1
   0   1   2
   0   0   0   0   1
   1   1   1
   0   1   0   1   2
   0   0   0   1   3
   0   0   0   0   0   0   1
   0   1   1   2   3
   0   0   0   0   0   0   0   0   0   0   1
   0   0   0   0   0   1   4
   0   0   0   1   0   2   5
For example, row 15 gives: s(32) = f(221) + 2f(2111) + 5f(11111).

Crossrefs

Row sums are A321893.

Cf. A000085, A008480, A056239, A082733, A124795, A153452, A296188, A300121, A321742-A321765.

Sequence in context: A357374 A264048 A101257 * A225542 A227009 A144629

Adjacent sequences: A321889 A321890 A321891 * A321893 A321894 A321895

Keyword

nonn,more,tabf

Author

Gus Wiseman, Nov 20 2018

Status

approved