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%I #11 Mar 06 2022 00:16:47

%S 1,0,2,0,2,3,0,0,9,4,0,0,6,24,5,0,0,0,40,50,6,0,0,0,20,150,90,7,0,0,0,

%T 0,175,420,147,8,0,0,0,0,70,840,980,224,9,0,0,0,0,0,756,2940,2016,324,

%U 10,0,0,0,0,0,252,4410,8400,3780,450,11

%N A007318^(-1) * A132813.

%C Row sums = A005773 starting (1, 2, 5, 13, 35, 96, ...).

%F Inverse binomial transform of A132813.

%e First few rows of the triangle:

%e 1;

%e 0, 2;

%e 0, 2, 3;

%e 0, 0, 9, 4;

%e 0, 0, 6, 24, 5;

%e 0, 0, 0, 40, 50, 6;

%e 0, 0, 0, 20, 150, 90, 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; for (n=1, nn, for (k=1, n, print1(t132814[n, k], ", ");););} \\ _Michel Marcus_, Feb 12 2014

%Y Cf. A132813, A005773.

%K nonn,tabl

%O 0,3

%A _Gary W. Adamson_, Sep 01 2007

%E More terms from _Michel Marcus_, Feb 12 2014