A385544 G.f. A(x) satisfies A(x) = 1 + Sum_{k>=1} k * x^k * A(k*x).
1, 1, 3, 10, 47, 309, 2846, 37021, 681653, 17809832, 661559047, 34979604911, 2635492535328, 283176079413813, 43418520087991775, 9505069880265893234, 2972315533856872301859, 1328214006502208982129889, 848461208731369665554869614, 775048547251487987362405899361
Offset: 0
Programs
-
Mathematica
a[0] = 1; a[n_] := a[n] = Sum[(n-k)^(k+1)*a[k], {k, 0, n-1}]; Table[a[n], {n, 0, 20}] (* Vaclav Kotesovec, Jul 03 2025 *) -
PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (i-j)^(j+1)*v[j+1])); v;
Formula
a(0) = 1; a(n) = Sum_{k=0..n-1} (n-k)^(k+1) * a(k).
From Vaclav Kotesovec, Jul 03 2025: (Start)
a(n) ~ c * 3^(n*(n-1)/6), where
c = 151875.34106580399103962024875... if mod(n,3) = 0,
c = 151875.34107021815371382907842... if mod(n,3) = 1,
c = 151875.34106681673681179782608... if mod(n,3) = 2. (End)