[seqfan] A269500

[Paul Curtz]

Hello,

Consider the difference table of A004146 with two 0's instead of one.

0,  0,  1,   5,  16,  45,  121,  320,   841, ...
0,  1,  4,  11,  29,  76,  199,  521,  1364, ...  = A269500(n) = 0, A002878(n)
1,  3,  7,  18,  47, 123,  322,  843,  2207, ...
2,  4, 11,  29,  76, 199,  521, 1364,  3571, ...
2,  7, 18,  47, 123, 322,  843, 2207,  5778, ...
5, 11, 29,  76, 199, 521, 1364, 3571,  9349, ...
6, 18, 47, 123, 322, 843, 2207, 5778, 15127, ...
etc.
First column (inverse binomial transform): 0, 0, A098600(n).
Second column: A000032(n) with 0 instead of 2.  
Third column: from A000032.
Interleave first and second line: O, O, A001350(n).
Interleave second and third line: 0, 1, 1, 3, 4, 7, 11, ... second column with one 1.

Paul