cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A321763 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of s(v) in m(u), where H is Heinz number, m is monomial symmetric functions, and s is Schur functions.

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%I A321763 #4 Nov 20 2018 19:46:06
%S A321763 1,1,1,-1,0,1,1,-1,1,0,1,-2,1,0,-1,1,-1,0,0,1,0,1,0,-1,1,0,-1,1,-1,2,
%T A321763 1,-1,0,0,1,-1,1,0,0,0,1,-3
%N A321763 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of s(v) in m(u), where H is Heinz number, m is monomial symmetric functions, and s is Schur functions.
%C A321763 Row n has length A000041(A056239(n)).
%C A321763 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A321763 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321763 Triangle begins:
%e A321763    1
%e A321763    1
%e A321763    1  -1
%e A321763    0   1
%e A321763    1  -1   1
%e A321763    0   1  -2
%e A321763    1   0  -1   1  -1
%e A321763    0   0   1
%e A321763    0   1   0  -1   1
%e A321763    0  -1   1  -1   2
%e A321763    1  -1   0   0   1  -1   1
%e A321763    0   0   0   1  -3
%e A321763 For example, row 10 gives: m(31) = -s(22) + s(31) - s(211) + 2s(1111).
%Y A321763 Row sums are A321764.
%Y A321763 Cf. A000085, A008480, A056239, A082733, A124795, A153452, A296188, A300121, A317554, A321742-A321765.
%K A321763 sign,more,tabf
%O A321763 1,12
%A A321763 _Gus Wiseman_, Nov 20 2018