A209238 G.f.: A(x) = Sum_{n>=0} x^n * A(n*x) / A(x)^n.

1, 1, 1, 1, 2, 6, 33, 261, 3125, 54281, 1360227, 49213679, 2551724168, 189734190172, 20202532257783, 3077389342754387, 670727373110373402, 209089605110085626174, 93228754516671937710239, 59465333534426105454885059, 54262238803939167296498684986

Offset: 0

Author

Paul D. Hanna, Jan 27 2013

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + x^2 + x^3 + 2*x^4 + 6*x^5 + 33*x^6 + 261*x^7 + 3125*x^8 +...
The table of coefficients of x^k in A(n*x)/A(x)^n begin:
  n=0: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...];
  n=1: [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...];
  n=2: [1, 0, 1, 2, 18, 128, 1704, 28908, 729461, 26121996, ...];
  n=3: [1, 0, 3, 8, 102, 1032, 20052, 502104, 18852177, ...];
  n=4: [1, 0, 6, 20, 333, 4404, 113292, 3769344, 188468286, ...];
  n=5: [1, 0, 10, 40, 825, 13504, 433060, 17986560, 1123704270, ...];
  n=6: [1, 0, 15, 70, 1725, 33684, 1294525, 64474290, ...];
  n=7: [1, 0, 21, 112, 3213, 72912, 3266599, 189725472, ...];
  n=8: [1, 0, 28, 168, 5502, 142296, 7282212, 483225336, ...];
  n=9: [1, 0, 36, 240, 8838, 256608, 14768652, 1102246128,  ...]; ...
This sequence equals the antidiagonal sums of the above table.
		

Crossrefs

Cf. A125282.

Programs

PARI

{a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=sum(k=0, n, x^k*subst(A,x,k*x +x*O(x^n))/A^(k))  );polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))