A331569 Array read by antidiagonals: A(n,k) is the number of binary matrices with k distinct columns and any number of distinct nonzero rows with n ones in every column and columns in decreasing lexicographic order.
1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 3, 0, 1, 0, 1, 17, 0, 0, 1, 0, 1, 230, 184, 0, 0, 1, 0, 1, 3264, 16936, 840, 0, 0, 1, 0, 1, 60338, 2711904, 768785, 0, 0, 0, 1, 0, 1, 1287062, 675457000, 1493786233, 21770070, 0, 0, 0, 1, 0, 1, 31900620, 232383728378, 5254074934990, 585810653616, 328149360, 0, 0, 0, 1
Offset: 0
Examples
Array begins: =============================================================== n\k | 0 1 2 3 4 5 6 ----+---------------------------------------------------------- 0 | 1 1 0 0 0 0 0 ... 1 | 1 1 1 1 1 1 1 ... 2 | 1 0 3 17 230 3264 60338 ... 3 | 1 0 0 184 16936 2711904 675457000 ... 4 | 1 0 0 840 768785 1493786233 5254074934990 ... 5 | 1 0 0 0 21770070 585810653616 30604798810581906 ... 6 | 1 0 0 0 328149360 161087473081920 ... ... The A(2,2) = 3 matrices are: [1 1] [1 0] [1 0] [1 0] [1 1] [0 1] [0 1] [0 1] [1 1]
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..209
Crossrefs
Programs
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PARI
WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)} D(p, n, k)={my(v=vector(n)); for(i=1, #p, v[p[i]]++); binomial(WeighT(v)[n], k)/prod(i=1, #v, i^v[i]*v[i]!)} T(n, k)={ my(m=n*k+1, q=Vec(exp(intformal(O(x^m) - x^n/(1-x)))), f=Vec(serlaplace(1/(1+x) + O(x*x^m))/(x-1))); if(n==0, k<=1, sum(j=1, m, my(s=0); forpart(p=j, s+=(-1)^#p*D(p, n, k), [1, n]); s*sum(i=j, m, q[i-j+1]*f[i]))); }
Comments