A129620 - OEIS

%I #21 Oct 23 2019 14:43:08

%S 1,1,0,1,1,0,1,2,1,0,1,2,5,1,0,1,2,8,9,1,0,1,2,8,24,17,1,0,1,2,8,32,

%T 74,26,1,0,1,2,8,32,140,189,41,1,0,1,2,8,32,167,542,460,57,1,0,1,2,8,

%U 32,167,837,1964,989,81,1,0,1,2,8,32,167,928,4167,6291,2021,106,1,0

%N Square array read by falling antidiagonals: T(n,k) is the number of connected directed multigraphs with loops with n arcs and at most k vertices.

%C Partial sums of the rows of A139621, i.e., T(n,k) = sum(A139621(n,p),p=0..k).

%H Andrew Howroyd, <a href="/A129620/b129620.txt">Table of n, a(n) for n = 0..1325</a>

%F T(n,2) = A138107(n,2) - floor(n/2).

%F If k >= n+1, T(n,k) = A137975(n).

%e 1  1  1  1  1  1  ...

%e 0  1  2  2  2  2  ...

%e 0  1  5  8  8  8  ...

%e 0  1  9 24 32 32  ...

%e 0  1  17  (...)

%e (...)

%Y Cf. A138107, A139621.

%K nonn,tabl

%O 0,8

%A _Benoit Jubin_, May 06 2008

%E Name edited by _M. F. Hasler_, Jul 31 2017

%E Terms a(32) and beyond from _Andrew Howroyd_, Oct 22 2019