A138765 - OEIS

%I #9 Apr 03 2022 22:52:42

%S 2,5,3,10,24,10,17,99,145,24,26,288,1090,840,65,37,675,5185,11880,

%T 4901,168,50,1368,18226,93024,129601,28560,441,65,2499,51985,491400,

%U 1669265,1413720,166465,1155,82,4224,127450,1964024,13249601,29953728,15421330

%N Triangle read by rows, derived from a(n) = N*a(n-1) + a(n-2).

%C Inverse sums of second array terms by rows = 1/1, 1/4, 1/9, 1/16, ...; =

%C Sum_{n>=1} 1/a(n) = Pi^2/6 = 1.6449340668...

%F Triangle read by rows, antidiagonals of a secondary array.

%F The first array = sequences of the form a(n) = N*a(n-1) + a(n-2).

%F   N = 1: 1, 1,  2,  3, ...;

%F   N = 2: 1, 2,  5, 12, ...;

%F   N = 3: 1, 3, 10, 33, ...;

%F   ...

%F The second array = (for N = 1,2,3,...) k(1)*k(3), k(2)*k(4), k(3)*k(5), ...:

%F    2,  3,   10,    24, ...

%F    5, 24,  145,   840, ...

%F   10, 99, 1090, 11880, ...

%F The triangle = antidiagonals of this second array.

%e First few rows of the triangle:

%e    2;

%e    5,    3;

%e   10,   24,    10;

%e   17,   99,   145,    24;

%e   26,  288,  1090,   840,     65;

%e   37,  675,  5185, 11880,   4901,   168;

%e   50, 1368, 18226, 93024, 129601, 28560, 442;

%e   ...

%K nonn,tabl

%O 1,1

%A _Gary W. Adamson_, Mar 30 2008