cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A057275 Triangle T(n,k) of number of unilaterally connected digraphs on n labeled nodes and with k arcs, k=0..n*(n-1).

Original entry on oeis.org

1, 0, 2, 1, 0, 0, 6, 20, 15, 6, 1, 0, 0, 0, 24, 222, 660, 908, 792, 495, 220, 66, 12, 1, 0, 0, 0, 0, 120, 2304, 15540, 52700, 109545, 161120, 182946, 167660, 125945, 77520, 38760, 15504, 4845, 1140, 190, 20, 1
Offset: 1

Views

Author

Vladeta Jovovic, Goran Kilibarda, Sep 14 2000

Keywords

Examples

			Triangle begins:
  [1],
  [0,2,1],
  [0,0,6,20,15,6,1],
  [0,0,0,0,24,222,660,908,792,495,220,66,12,1],
  ...
The number of unilaterally connected digraphs on 3 labeled nodes is 48 = 6+20+15+6+1.
		

Crossrefs

Row sums give A003029.
The unlabeled version is A057270.

Programs

  • PARI
    \\ See A057273 for Strong.
    Unilaterally(n, e=2)={my(u=vector(n), s=Strong(n,e)); for(n=1, #u, u[n]=vector(n, k, binomial(n,k)*s[k]*if(k==n, 1, sum(j=1, n-k, e^(k*(n-k-j))*(e^(k*j)-1)*u[n-k][j])))); vector(#u, n, vecsum(u[n]))}
    row(n)={Vecrev(Unilaterally(n, 1+'y)[n])}
    { for(n=1, 5, print(row(n))) } \\ Andrew Howroyd, Jan 19 2022