0,5

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.

First few rows of the array are:

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 are:

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;

Let M = 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.

In the array, antidiagonal terms (1, 3, 5, 1) become row 3 of the triangle.

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

Sequence in context: A143327 A094954 A083064 this_sequence A111672 A128198 A123349

Adjacent sequences: A112335 A112336 A112337 this_sequence A112339 A112340 A112341

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 04 2005