A321759 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of s(v) in h(u), where H is Heinz number, h is homogeneous symmetric functions, and s is Schur functions.

1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 2, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0

Offset

1,19

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..42.

Wikipedia, Symmetric polynomial

Example

Triangle begins:
   1
   1
   1   0
   1   1
   1   0   0
   1   1   0
   1   0   0   0   0
   1   2   1
   1   1   1   0   0
   1   0   1   0   0
   1   0   0   0   0   0   0
   1   1   2   1   0
For example, row 12 gives: h(211) = s(4) + s(22) + 2s(31) + s(211).

Crossrefs

Row sums are A321757.

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

Sequence in context: A093658 A096493 A269242 * A076882 A229745 A339366

Adjacent sequences: A321756 A321757 A321758 * A321760 A321761 A321762

Keyword

nonn,more,tabf

Author

Gus Wiseman, Nov 20 2018

Status

approved