A112338 Triangle read by rows, generated from A001263.

1, 1, 1, 1, 2, 1, 1, 3, 5, 1, 1, 4, 12, 14, 1, 1, 5, 22, 57, 42, 1, 1, 6, 35, 148, 303, 132, 1, 1, 7, 51, 305, 1144, 1743, 429, 1, 8, 70, 546, 3105, 9784, 10629, 1430, 1

Offset

0,5

Comments

Rows of the array are row sums of n-th powers of the Narayana triangle; e.g., row 1 = A000108: (1, 2, 5, 14, 42, ...); row 2 = row sums of the Narayana triangle squared (A103370): (1, 3, 12, 57, 303, ...), etc.

Links

Table of n, a(n) for n=0..43.

Formula

Let M be the infinite lower triangular Narayana triangle (A001263). Perform M^n * [1 0 0 0 ...] getting an array. Take antidiagonals of the array which become rows of the triangle A112338.

Example

In the array, antidiagonal terms (1, 3, 5, 1) become row 3 of the triangle.
First few rows of the array:
  1, 1,  1,   1,    1,     1, ...
  1, 2,  5,  14,   42,   132, ...
  1, 3, 12,  57,  303,  1743, ...
  1, 4, 22, 148, 1144,  9784, ...
  1, 5, 35, 305, 3105, 35505, ...
First few rows of the triangle:
  1;
  1, 1;
  1, 2,  1;
  1, 3,  5,   1;
  1, 4, 12,  14,   1;
  1, 5, 22,  57,  42,   1;
  1, 6, 35, 148, 303, 132, 1;

Crossrefs

Cf. A001263, A000326, A005915, A095266, A000108, A103370.

Sequence in context: A204057 A335975 A241578 * A111672 A323206 A340968

Adjacent sequences: A112335 A112336 A112337 * A112339 A112340 A112341

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 04 2005

Status

approved