A382100 - OEIS

A382100

Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of 1/(2 - B_k(x)), where B_k(x) = 1 + x*B_k(x)^k.

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 4, 1, 1, 1, 4, 10, 8, 1, 1, 1, 5, 19, 35, 16, 1, 1, 1, 6, 31, 98, 126, 32, 1, 1, 1, 7, 46, 213, 531, 462, 64, 1, 1, 1, 8, 64, 396, 1556, 2974, 1716, 128, 1, 1, 1, 9, 85, 663, 3651, 11843, 17060, 6435, 256, 1

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OFFSET

0,9

LINKS

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

FORMULA

A(n,k) = ( binomial(k*n,n) - (k-2) * Sum_{j=0..n-1} binomial(k*n,j) )/2 for n > 0.

G.f. of column k: 1/( 1 - Series_Reversion( x/(1+x)^k ) ).

EXAMPLE

Square array begins:

1, 1, 1, 1, 1, 1, 1, ...

1, 2, 3, 4, 5, 6, 7, ...