cp's OEIS Frontend

A255768 Triangle read by rows: T(n,k) = total number of parts in all partitions of n into k distinct parts.

%I A255768 #36 Dec 18 2015 09:47:46
%S A255768 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 A255768 120,9,28,158,189,24,14,208,283,51,24,259,390,107,24,284,582,173,5,31,
%U A255768 361,749,311,11,18,409,1024,485,29,39,488,1289,767,61
%N A255768 Triangle read by rows: T(n,k) = total number of parts in all partitions of n into k distinct parts.
%C A255768 Column 1 is sigma = A000203.
%C A255768 Column 2 is A216669.
%C A255768 Row sums give A006128.
%C A255768 Row n has length A003056(n) hence the first element of column k is in row A000217(n).
%C A255768 The first positive element in column k is k.
%H A255768 Alois P. Heinz, <a href="/A255768/b255768.txt">Rows n = 1..500, flattened</a>
%F A255768 T(n,1) = A000203(n).
%e A255768 Triangle begins:
%e A255768    1;
%e A255768    3;
%e A255768    4,   2;
%e A255768    7,   5;
%e A255768    6,  14;
%e A255768   12,  20,    3;
%e A255768    8,  39,    7;
%e A255768   15,  52,   19;
%e A255768   13,  74,   41;
%e A255768   18, 102,   68,    4;
%e A255768   12, 134,  120,    9;
%e A255768   28, 158,  189,   24;
%e A255768   14, 208,  283,   51;
%e A255768   24, 259,  390,  107;
%e A255768   24, 284,  582,  173,   5;
%e A255768   31, 361,  749,  311,  11;
%e A255768   18, 409, 1024,  485,  29;
%e A255768   39, 488, 1289,  767,  61;
%e A255768   20, 538, 1699, 1114, 127;
%e A255768   42, 634, 2092, 1624, 238;
%e A255768   32, 678, 2642, 2291, 403, 6;
%e A255768   ...
%Y A255768 Cf. A000041, A000203, A000217, A006128, A003056, A116608, A216669, A255767.
%K A255768 nonn,tabf,look
%O A255768 1,2
%A A255768 _Omar E. Pol_, May 21 2015
%E A255768 a(27) and beyond from _Alois P. Heinz_, Jul 26 2015