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A124469 Triangle, read by rows, where row n equals the inverse binomial transform of column n in the rectangular table A124460. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified April 23 18:34 EDT 2019. Contains 322387 sequences. (Running on oeis4.)