A308460 - OEIS

A308460

Square array A(n,k), n >= 1, k >= 1, read by antidiagonals, where column k is the expansion of e.g.f. log(Sum_{j>=0} k^binomial(j,2) * x^j/j!).

%I #14 May 29 2019 12:04:23

%S 1,1,0,1,1,0,1,2,4,0,1,3,20,38,0,1,4,54,624,728,0,1,5,112,3834,55248,

%T 26704,0,1,6,200,15104,1027080,13982208,1866256,0,1,7,324,45750,

%U 9684224,1067308488,10358360640,251548592,0,1,8,490,116208,60225000,30458183680,4390480193904,22792648882176,66296291072,0

%N Square array A(n,k), n >= 1, k >= 1, read by antidiagonals, where column k is the expansion of e.g.f. log(Sum_{j>=0} k^binomial(j,2) * x^j/j!).

%H Seiichi Manyama, <a href="/A308460/b308460.txt">Antidiagonals n = 1..50, flattened</a>

%e Square array begins:

%e 1, 1, 1, 1, 1, ...

%e 0, 1, 2, 3, 4, ...

%e 0, 4, 20, 54, 112, ...

%e 0, 38, 624, 3834, 15104, ...

%e 0, 728, 55248, 1027080, 9684224, ...

%e 0, 26704, 13982208, 1067308488, 30458183680, ...

%Y Columns k=1..4 give A000007(n-1), A001187, A054941, A003027.

%K nonn,tabl

%O 1,8

%A _Seiichi Manyama_, May 28 2019