A124469 Triangle, read by rows, where row n equals the inverse binomial transform of column n in the rectangular table A124460.

1, 1, 1, 1, 3, 1, 1, 8, 6, 1, 1, 22, 28, 11, 1, 1, 65, 120, 81, 20, 1, 1, 209, 500, 494, 219, 37, 1, 1, 730, 2088, 2733, 1812, 578, 70, 1, 1, 2743, 8884, 14411, 12904, 6299, 1518, 135, 1, 1, 10958, 38803, 74484, 84424, 56590, 21384, 4007, 264, 1, 1, 46057, 174366

Offset

0,5

Comments

In table A124460, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = Sum_{k>=0} y^k * R_k(y)^n for n>=0.

Links

Table of n, a(n) for n=0..57.

Formula

Secondary diagonal T(n+1,n) = 2^n + n = A006127(n).

Example

Triangle begins:
1;
1, 1;
1, 3, 1;
1, 8, 6, 1;
1, 22, 28, 11, 1;
1, 65, 120, 81, 20, 1;
1, 209, 500, 494, 219, 37, 1;
1, 730, 2088, 2733, 1812, 578, 70, 1;
1, 2743, 8884, 14411, 12904, 6299, 1518, 135, 1;
1, 10958, 38803, 74484, 84424, 56590, 21384, 4007, 264, 1;
1, 46057, 174366, 383391, 526121, 453082, 238853, 72076, 10693, 521, 1;

Prog

(PARI) {T(n, k)=local(R=vector(n+2, r, vector(n+2, c, binomial(r+c-2, c-1)))); for(i=0, n, for(r=0, n, R[r+1]=Vec(sum(c=0, n, x^c*Ser(R[c+1])^r+O(x^(n+1)))))); Vec(subst(Ser(vector(n+1, j, R[j][n+1])), x, x/(1+x))/(1+x))[k+1]}

Crossrefs

Cf. A124470 (row sums), A006127 (diagonal T(n+1, n)); A124460 (table).

Sequence in context: A091698 A134380 A263859 * A094816 A097712 A238688

Adjacent sequences: A124466 A124467 A124468 * A124470 A124471 A124472

Keyword

nonn,tabl

Author

Paul D. Hanna, Nov 03 2006

Status

approved