A255768 - OEIS

%I #36 Dec 18 2015 09:47:46

%S 1,3,4,2,7,5,6,14,12,20,3,8,39,7,15,52,19,13,74,41,18,102,68,4,12,134,

%T 120,9,28,158,189,24,14,208,283,51,24,259,390,107,24,284,582,173,5,31,

%U 361,749,311,11,18,409,1024,485,29,39,488,1289,767,61

%N Triangle read by rows: T(n,k) = total number of parts in all partitions of n into k distinct parts.

%C Column 1 is sigma = A000203.

%C Column 2 is A216669.

%C Row sums give A006128.

%C Row n has length A003056(n) hence the first element of column k is in row A000217(n).

%C The first positive element in column k is k.

%H Alois P. Heinz, <a href="/A255768/b255768.txt">Rows n = 1..500, flattened</a>

%F T(n,1) = A000203(n).

%e Triangle begins:

%e    1;

%e    3;

%e    4,   2;

%e    7,   5;

%e    6,  14;

%e   12,  20,    3;

%e    8,  39,    7;

%e   15,  52,   19;

%e   13,  74,   41;

%e   18, 102,   68,    4;

%e   12, 134,  120,    9;

%e   28, 158,  189,   24;

%e   14, 208,  283,   51;

%e   24, 259,  390,  107;

%e   24, 284,  582,  173,   5;

%e   31, 361,  749,  311,  11;

%e   18, 409, 1024,  485,  29;

%e   39, 488, 1289,  767,  61;

%e   20, 538, 1699, 1114, 127;

%e   42, 634, 2092, 1624, 238;

%e   32, 678, 2642, 2291, 403, 6;

%e   ...

%Y Cf. A000041, A000203, A000217, A006128, A003056, A116608, A216669, A255767.

%K nonn,tabf,look

%O 1,2

%A _Omar E. Pol_, May 21 2015

%E a(27) and beyond from _Alois P. Heinz_, Jul 26 2015