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.

A321897 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of p(v) in h(u) * Product_i u_i!, where H is Heinz number, h is homogeneous symmetric functions, and p is power sum symmetric functions.

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%I A321897 #5 Nov 21 2018 09:24:53
%S A321897 1,1,1,1,0,1,2,3,1,0,1,1,6,3,8,6,1,0,0,1,0,1,0,2,1,0,0,2,3,1,24,30,20,
%T A321897 15,20,10,1,0,0,0,1,1,120,90,144,40,15,90,120,45,40,15,1,0,6,0,3,8,6,
%U A321897 1,0,0,2,3,2,4,1,0,0,0,0,1,720,840,504,420,630
%N A321897 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of p(v) in h(u) * Product_i u_i!, where H is Heinz number, h is homogeneous symmetric functions, and p is power sum symmetric functions.
%C A321897 Row n has length A000041(A056239(n)).
%C A321897 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A321897 Wikipedia, <a href="https://en.wikipedia.org/wiki/Symmetric_polynomial">Symmetric polynomial</a>
%e A321897 Triangle begins:
%e A321897     1
%e A321897     1
%e A321897     1    1
%e A321897     0    1
%e A321897     2    3    1
%e A321897     0    1    1
%e A321897     6    3    8    6    1
%e A321897     0    0    1
%e A321897     0    1    0    2    1
%e A321897     0    0    2    3    1
%e A321897    24   30   20   15   20   10    1
%e A321897     0    0    0    1    1
%e A321897   120   90  144   40   15   90  120   45   40   15    1
%e A321897     0    6    0    3    8    6    1
%e A321897     0    0    2    3    2    4    1
%e A321897     0    0    0    0    1
%e A321897   720  840  504  420  630  504  210  280  105  210  420  105   70   21    1
%e A321897     0    0    0    1    0    2    1
%e A321897 For example, row 14 gives: 12h(41) = 6p(41) + 3p(221) + 8p(311) + 6p(2111) + p(11111).
%Y A321897 Row sums are A321898.
%Y A321897 Cf. A005651, A008480, A056239, A124794, A124795, A319193, A321742-A321765, A321896.
%K A321897 nonn,tabf
%O A321897 1,7
%A A321897 _Gus Wiseman_, Nov 20 2018