A321756 - OEIS

%I #4 Nov 20 2018 16:31:16

%S 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,

%T 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,

%U 2,3,3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1

%N 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.

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

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

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>

%e Triangle begins:

%e    1

%e    1

%e    0   1

%e    1   1

%e    0   0   1

%e    0   1   1

%e    0   0   0   0   1

%e    1   2   1

%e    0   1   0   1   1

%e    0   0   0   1   1

%e    0   0   0   0   0   0   1

%e    0   1   1   2   1

%e    0   0   0   0   0   0   0   0   0   0   1

%e    0   0   0   0   0   1   1

%e    0   0   0   1   0   1   1

%e    1   2   3   3   1

%e    0   0   0   0   0   0   0   0   0   0   0   0   0   0   1

%e    0   0   1   2   1   2   1

%e For example, row 18 gives: e(221) = s(32) + 2s(221) + s(311) + 2s(2111) + s(11111).

%Y Row sums are A321757.

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

%K nonn,tabf

%O 1,19

%A _Gus Wiseman_, Nov 20 2018