cp's OEIS Frontend

A133088 A007318^(-1) * A133080.

%I A133088 #19 Mar 07 2022 07:53:40
%S A133088 1,0,1,-1,-2,1,2,3,-2,1,-3,-4,2,-4,1,4,5,0,10,-4,1,-5,-6,-5,-20,9,-6,
%T A133088 1,6,7,14,35,-14,21,-6,1,-7,-8,-28,-56,14,-56,20,-8,1,8,9,48,84,0,126,
%U A133088 -48,36,-8,1,-9,-10,-75,-120,-42,-252,90,-120,35,-10,1
%N A133088 A007318^(-1) * A133080.
%C A133088 Row sums give A123344.
%C A133088 Inverse binomial transform of A133080.
%e A133088 First few rows of the triangle:
%e A133088    1;
%e A133088    0,   1;
%e A133088   -1,  -2,   1;
%e A133088    2,   3,  -2,   1;
%e A133088   -3,  -4,   2,  -4,   1;
%e A133088    4,   5,   0,  10,  -4,   1;
%e A133088   -5,  -6,  -5, -20,   9,  -6,   1;
%e A133088   ...
%o A133088 (PARI) tabl(nn) = {t007318 = matrix(nn, nn, n, k, binomial(n-1, k-1)); t133080 = matrix(nn, nn, n, k, if (k==n, 1, if (k == (n-1), 1 - (n % 2), 0))); t133088 = t007318^(-1)*t133080; for (n = 1, nn, for (k = 1, n, print1(t133088[n, k], ", ");); print(););} \\ _Michel Marcus_, Feb 13 2014
%Y A133088 Cf. A133080, A007318.
%K A133088 tabl,sign
%O A133088 0,5
%A A133088 _Gary W. Adamson_, Sep 08 2007
%E A133088 Typo corrected by _Travis Hoppe_, Apr 24 2008
%E A133088 One term's sign corrected by _Michel Marcus_, Feb 13 2014