A138765 Triangle read by rows, derived from a(n) = N*a(n-1) + a(n-2).

2, 5, 3, 10, 24, 10, 17, 99, 145, 24, 26, 288, 1090, 840, 65, 37, 675, 5185, 11880, 4901, 168, 50, 1368, 18226, 93024, 129601, 28560, 441, 65, 2499, 51985, 491400, 1669265, 1413720, 166465, 1155, 82, 4224, 127450, 1964024, 13249601, 29953728, 15421330

Offset

1,1

Comments

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

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

Links

Table of n, a(n) for n=1..43.

Formula

Triangle read by rows, antidiagonals of a secondary array.

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

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

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

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

...

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

2, 3, 10, 24, ...

5, 24, 145, 840, ...

10, 99, 1090, 11880, ...

The triangle = antidiagonals of this second array.

Example

First few rows of the triangle:
   2;
   5,    3;
  10,   24,    10;
  17,   99,   145,    24;
  26,  288,  1090,   840,     65;
  37,  675,  5185, 11880,   4901,   168;
  50, 1368, 18226, 93024, 129601, 28560, 442;
  ...

Crossrefs

Sequence in context: A101492 A297442 A277709 * A097753 A120860 A259971

Adjacent sequences: A138762 A138763 A138764 * A138766 A138767 A138768

Keyword

nonn,tabl

Author

Gary W. Adamson, Mar 30 2008

Status

approved