0,4

Row sums = A000293, solid partitions: (1, 1, 4, 10, 26, 59, 140, 307, 684,...)

Triangle by rows, A000041 convolved with A002836: (1, 0, 2, 5, 12, 24, 56,...). Antidiagonals of a convolution array, A002836 * A000041: 1, . 1, . 2, . 3, . 5, . 7, . 11,... 0, . 0, . 0, . 0, . 0, . 0, .. 0,... 2, . 2, . 4, . 6, .10, .14, ..22,... 5, . 5, . 10, .15, .25, .35, ..55,... 12 .12, . 24, .36, .60, .84, .132,... ...

First few rows of the triangle =

1;

0, 1;

2, 0, 2;

5, 2, 0, 3;

12, 5, 4, 0, 5;

24, 12, 10, 6, 0, 7;

56, 24, 24, 15, 10, 0, 11;

113, 56, 48, 36, 25, 14, 0, 15;

248, 113, 112, 72, 60, 35, 22, 0, 22;

503, 248, 226, 168, 120, 84, 55, 30, 0, 30;

...

Example: row 4 = (12, 5, 4, 0, 5), sum = 26 = A000293(4).

Cf. A000293, A000041, A002836

Sequence in context: A052438 A158855 A005074 this_sequence A078182 A133394 A094721

Adjacent sequences: A161561 A161562 A161563 this_sequence A161565 A161566 A161567

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2009