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%I #21 Jun 26 2022 13:03:25
%S 1,-1,2,1,-2,3,-1,0,0,4,1,4,-12,8,5,-1,-10,30,-40,25,6,1,18,-45,60,
%T -75,54,7,-1,-28,42,0,0,-84,98,8,1,40,0,-224,420,-336,0,160,9,-1,-54,
%U -108,672,-1260,1512,-1176,288,243,10
%N A007318^(-1) * A132814.
%C Row sums = A001405: (1, 1, 2, 3, 6, 10, 10, ...).
%F Inverse binomial transform of A132814.
%e First few rows of the triangle:
%e 1;
%e -1, 2;
%e 1, -2, 3;
%e -1, 0, 0, 4;
%e 1, 4, -12, 8, 5;
%e -1, -10, 30, -240, 25, 6;
%e 1, 18, -45, 60, -75, 54, 7;
%e ...
%o (PARI) tabl(nn) = {t007318 = matrix(nn, nn, n, k, binomial(n-1, k-1)); t132813 = matrix(nn, nn, n, k, binomial(n-1, k-1)*binomial(n, k-1)); t132814 = t007318^(-1)*t132813; t132815 = t007318^(-1)*t132814; for (n=1, nn, for (k=1, n, print1(t132815[n, k], ", ");););} \\ _Michel Marcus_, Feb 12 2014
%Y Cf. A001405, A007318, A132814.
%K tabl,easy,sign
%O 0,3
%A _Gary W. Adamson_, Sep 01 2007
%E Typo corrected by _Travis Hoppe_, Apr 24 2008
%E T(5, 1) corrected by _Michel Marcus_, Feb 12 2014
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