This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A161564 #5 Jun 02 2025 01:44:26 %S A161564 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, %T A161564 113,56,48,36,25,14,0,15,248,113,112,72,60,35,22,0,22,503,248,226,168, %U A161564 120,84,55,30,0,30 %N A161564 Convolution triangle for A000293 (solid partitions): A000041 * A002836. %C A161564 Row sums = A000293, solid partitions: (1, 1, 4, 10, 26, 59, 140, 307, 684,...) %F A161564 Triangle read 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,... ... %e A161564 First few rows of the triangle = %e A161564 1; %e A161564 0, 1; %e A161564 2, 0, 2; %e A161564 5, 2, 0, 3; %e A161564 12, 5, 4, 0, 5; %e A161564 24, 12, 10, 6, 0, 7; %e A161564 56, 24, 24, 15, 10, 0, 11; %e A161564 113, 56, 48, 36, 25, 14, 0, 15; %e A161564 248, 113, 112, 72, 60, 35, 22, 0, 22; %e A161564 503, 248, 226, 168, 120, 84, 55, 30, 0, 30; %e A161564 ... %e A161564 Example: row 4 = (12, 5, 4, 0, 5), sum = 26 = A000293(4). %Y A161564 Cf. A000293, A000041, A002836 %K A161564 nonn,tabl %O A161564 0,4 %A A161564 _Gary W. Adamson_, Jun 13 2009