cp's OEIS Frontend

A329819 Triangular array, read by rows: T(n,k) = [(x*y*z)^k] (-1 + (1 + x + 1/x)*(1 + y + 1/y)*(1 + z + 1/z))^n for -n <= k <= n.

%I A329819 #18 Nov 22 2019 05:27:29
%S A329819 1,1,0,1,1,6,26,6,1,1,24,195,264,195,24,1,1,60,898,3276,5646,3276,898,
%T A329819 60,1,1,120,3065,22260,72730,101520,72730,22260,3065,120,1,1,210,8526,
%U A329819 105690,581475,1510860,2103740,1510860,581475,105690,8526,210,1
%N A329819 Triangular array, read by rows: T(n,k) = [(x*y*z)^k] (-1 + (1 + x + 1/x)*(1 + y + 1/y)*(1 + z + 1/z))^n for -n <= k <= n.
%H A329819 Seiichi Manyama, <a href="/A329819/b329819.txt">Rows n = 0..25, flattened</a>
%F A329819 T(n,k) = T(n,-k).
%e A329819 Triangle begins:
%e A329819                                  1;
%e A329819                          1,      0,     1;
%e A329819                   1,     6,     26,     6,     1;
%e A329819            1,    24,   195,    264,   195,    24,    1;
%e A329819      1,   60,   898,  3276,   5646,  3276,   898,   60,   1;
%e A329819 1, 120, 3065, 22260, 72730, 101520, 72730, 22260, 3065, 120, 1;
%o A329819 (PARI) {T(n, k) = polcoef(polcoef(polcoef((-1+(1+x+1/x)*(1+y+1/y)*(1+z+1/z))^n, k), k), k)}
%Y A329819 T(n,0) gives A328874.
%Y A329819 Cf. A260492, A329816, A329820.
%K A329819 nonn,tabf
%O A329819 0,6
%A A329819 _Seiichi Manyama_, Nov 21 2019