A114280 A triangle related to the Sierpinski related number triangle A114278.

1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 2, 3, 1, 1, 1, 3, 7, 4, 5, 1, 1, 3, 8, 6, 11, 3, 1, 1, 4, 14, 14, 35, 14, 7, 1, 1, 4, 14, 14, 35, 14, 7, 1, 1, 1, 5, 22, 28, 91, 49, 35, 8, 9, 1, 1, 5, 23, 32, 119, 77, 70, 22, 37, 5, 1

Offset

0,8

Comments

Constructed as follows: Take inverse binomial transform of square array associated to A114278. Multiply by diagonal matrix with reciprocal of Gould numbers A001316 on diagonal. Transpose. The k-th column of A114278 has g.f. given by x^k*sum{j=0..k, A001316(j)*A114280(k,j)*x^j/(1-x)^(j+1)}. Row sums are A114281. Inverse has row sums 0^n (conjecture).

Links

Table of n, a(n) for n=0..65.

Example

Triangle begins
1;
1, 1;
1, 1, 1;
1, 2, 3, 1;
1, 2, 3, 1, 1;
1, 3, 7, 4, 5, 1;
1, 3, 8, 6,11, 3, 1;
1, 4,14,14,35,14, 7, 1;
1, 4,14,14,35,14, 7, 1, 1;

Crossrefs

Sequence in context: A284050 A308644 A308184 * A123564 A036466 A065882

Adjacent sequences: A114277 A114278 A114279 * A114281 A114282 A114283

Keyword

nonn,tabl

Author

Paul Barry, Nov 20 2005

Status

approved