A162507 - OEIS

%I #5 Sep 28 2016 06:38:50

%S 1,2,1,2,3,1,4,3,4,1,4,9,4,5,1,6,12,12,5,6,1,6,18,24,15,6,7,1,8,24,36,

%T 30,18,7,8,1,8,33,60,60,36,21,8,9,1,10,39,88,95,72,42,24,9,10,1,10,51,

%U 124,160,138,84,48,27,10,11

%N Triangle read by rows, finite differences of an array generated by an infinite product (Cf. A162506).

%C Row sums = A162506 starting (1, 3, 6, 12, 23, 42, 77,...).

%F Given the infinite product and array shown in A162506, we have

%F a = [1,1,1,...], b = [1,0,2,0,2,0,2,...], c = [1,0,0,3,0,0,3,0,0,3,...];

%F The array is a, a*b, a*b*c,... Finite differences of array columns = rows of the triangle, deleting the first "1".

%e The array =

%e 1,...1,...1,...1,...1,...; = a

%e 1,...1,...3,...3,...5,...; = a*b

%e 1,...1,...3,...6,...8,...; = a*b*c

%e 1,...1,...3,...6,..12,...; = a*b*c*d

%e ...

%e taking finite differences from the top, then discarding the first "1",

%e we obtain triangle A162507:

%e 1;

%e 1, 2;

%e 1, 2, 3;

%e 1, 4, 3, 4;

%e 1, 4, 9, 4, 5;

%e 1, 6, 12, 12, 5, 6;

%e 1, 6, 18, 24, 15, 6, 7;

%e 1, 8, 24, 36, 30, 18, 7, 8;

%e 1, 8, 33, 60, 60, 36, 21, 8, 9;

%e 1, 10, 39, 88, 95, 72, 42, 24, 9, 10;

%e 1, 10, 51, 124, 160, 138, 84, 48, 27, 10, 11;

%e ...

%Y Cf. A162506.

%K nonn,tabl

%O 2,2

%A _Gary W. Adamson_, Jul 04 2009