%I
%S 1,2,2,3,4,4,4,6,8,8,5,8,12,16,16,6,10,16,24,32,32,7,12,20,32,48,64,
%T 64,8,14,24,40,64,96,128,128,9,16,28,48,80,128,192,256,256,10,18,32,
%U 56,96,160,256,384,512,512,11,20,36,64,112,192,320,512,768,1024,1024
%N Triangle read by rows: T(n,k) = (n  k + 1)*2^(k1).
%C T(n,k) is the number of paths from node 0 to odd k in a directed graph with 2n+1 vertices labeled 0, 1, ..., 2n+1 and edges leading from i to i+1 for all i, from i to i+2 for even i, and from i to i2 for odd i.  _Grace Work_, Mar 01 2020
%H Andrew Howroyd, <a href="/A130128/b130128.txt">Table of n, a(n) for n = 1..1275</a>
%H E. Krom and M. M. Roughan, <a href="http://girlsangle.org/page/bulletinarchive/GABv13n03E.pdf">Path Counting and Eulerian Numbers</a>, Girls' Angle Bulletin, Vol. 13, No. 3 (2020), 810.
%F Equals A004736 * A130123 as infinite lower triangular matrices.
%e First few rows of the triangle are:
%e 1;
%e 2, 2;
%e 3, 4, 4;
%e 4, 6, 8, 8;
%e 5, 8, 12, 16, 16;
%e 6, 10, 16, 24, 32, 32;
%e 7, 12, 20, 32, 48, 64, 64;
%e ...
%t Table[(n  k + 1)*2^(k  1), {n, 11}, {k, n}] // Flatten (* _Michael De Vlieger_, Mar 23 2020 *)
%o (PARI) T(n,k)={(n  k + 1)*2^(k1)} \\ _Andrew Howroyd_, Mar 01 2020
%Y Row sums are A000295.
%Y Cf. A004736, A130123.
%K nonn,tabl,walk
%O 1,2
%A _Gary W. Adamson_, May 11 2007
%E Name clarified by _Grace Work_, Mar 01 2020
%E Terms a(56) and beyond from _Andrew Howroyd_, Mar 01 2020
