A321756 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of s(v) in e(u), where H is Heinz number, e is elementary symmetric functions, and s is Schur functions.

1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 2, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 2, 3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

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..87.

Wikipedia, Symmetric polynomial

Example

Triangle begins:
   1
   1
   0   1
   1   1
   0   0   1
   0   1   1
   0   0   0   0   1
   1   2   1
   0   1   0   1   1
   0   0   0   1   1
   0   0   0   0   0   0   1
   0   1   1   2   1
   0   0   0   0   0   0   0   0   0   0   1
   0   0   0   0   0   1   1
   0   0   0   1   0   1   1
   1   2   3   3   1
   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1
   0   0   1   2   1   2   1
For example, row 18 gives: e(221) = s(32) + 2s(221) + s(311) + 2s(2111) + s(11111).

Crossrefs

Row sums are A321757.

Cf. A000085, A008480, A056239, A082733, A124795, A153452, A296188, A300121, A304438, A317552, A317554, A319225, A319226, A321742-A321765.

Sequence in context: A079748 A368457 A073368 * A258141 A037889 A339872

Adjacent sequences: A321753 A321754 A321755 * A321757 A321758 A321759

Keyword

nonn,tabf

Author

Gus Wiseman, Nov 20 2018

Status

approved