A124539 Triangle, read by rows, where row n equals the inverse binomial transform of column n in the rectangular table A124530.

1, 1, 0, 1, 1, 0, 1, 4, 1, 0, 1, 15, 8, 1, 0, 1, 61, 51, 14, 1, 0, 1, 273, 311, 138, 24, 1, 0, 1, 1331, 1901, 1191, 349, 42, 1, 0, 1, 6977, 11838, 9693, 4100, 868, 76, 1, 0, 1, 38872, 75556, 76950, 43257, 13459, 2163, 142, 1, 0, 1, 228089, 495146, 606275, 430517

Offset

0,8

Comments

In table A124530, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = Sum_{k>=0} y^k*R_k(y)^(n*k) for n>=0.

Links

Table of n, a(n) for n=0..59.

Formula

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

Example

Triangle begins:
1;
1, 0;
1, 1, 0;
1, 4, 1, 0;
1, 15, 8, 1, 0;
1, 61, 51, 14, 1, 0;
1, 273, 311, 138, 24, 1, 0;
1, 1331, 1901, 1191, 349, 42, 1, 0;
1, 6977, 11838, 9693, 4100, 868, 76, 1, 0;
1, 38872, 75556, 76950, 43257, 13459, 2163, 142, 1, 0;
1, 228089, 495146, 606275, 430517, 180000, 43274, 5442, 272, 1, 0; ...

Prog

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

Crossrefs

Cf. A124530 (table).

Sequence in context: A294522 A058710 A281891 * A351703 A369923 A249094

Adjacent sequences: A124536 A124537 A124538 * A124540 A124541 A124542

Keyword

nonn,tabl

Author

Paul D. Hanna, Nov 05 2006

Status

approved