A179380 - OEIS

%I #4 Mar 31 2012 13:23:39

%S 1,1,1,2,1,1,6,2,1,1,1,22,6,2,2,1,1,1,92,22,6,4,6,2,1,2,1,1,1,426,92,

%T 22,12,22,6,4,2,6,2,1,2,1,1,1,2146,426,92,44,36,92,22,12,6,4,22,6,4,2,

%U 1,6,2,1,2,1,1,1,11624,2146,426,184,132,426,92,44,36,22,12,8,92,22,12

%N Triangle T(n,k) read by rows: product of A074664(a_i) of all parts a_i of the k-th partition of n.

%C Row n has A000041(n) elements, sorted in Abramowitz-Stegun order.

%F A048996(n,k)* T(n,k) = A179313(n,k).

%F sum_{k=1.. A000041(n)} T(n,k) = A179379(n).

%F T(n,1) = A074664(n).

%e T(6,4) refers to the 4th partition of 6, 3+3. T(6,4)=A074664(3)*A074664(3)=2*2.

%e T(7,3) refers to the 3rd partition of 7, 2+5. T(7,3)=A074664(2)*A074664(5)=1*22.

%e The triangle starts

%e 1;

%e 1,1;

%e 2,1,1;

%e 6,2,1,1,1;

%e 22,6,2,2,1,1,1;

%e 92,22,6,4,6,2,1,2,1,1,1;

%e 426,92,22,12,22,6,4,2,6,2,1,2,1,1,1;

%Y Cf. A000041, A179379, A074664.

%K nonn,tabf

%O 1,4

%A _Alford Arnold_, Jul 12 2010

%E Edited and extended by _R. J. Mathar_, Jul 16 2010