%I A125282
%S A125282 1,1,2,5,17,80,525,4839,62936,1158785,30277579,1124649526,59465788597,
%T A125282 4480380804517,481401971074410,73812092299235769,16158739669470307453,
%U A125282 5052972095683109687920,2257981256268589345121153
%N A125282 G.f. satisfies: A(x) = Sum{n>=0} x^n * A(n*x).
%F A125282 a(n) = Sum_{k=0..n-1} (n-k)^k * a(k) for n>0 with a(0)=1.
%e A125282 A(x) = 1 + x + 2*x^2 + 5*x^3 + 17*x^4 + 80*x^5 + 525*x^6 + 4839*x^7 +...
%e A125282 G.f. A(x) satisfies:
%e A125282 A(x) = 1 + x*A(x) + x^2*A(2x) + x^3*A(3x) + x^4*A(4x) + x^5*A(5x) +...
%e A125282 which leads to the recurrence illustrated by:
%e A125282 a(4) = 4^0*(1) + 3^1*(1) + 2^2*(2) + 1^3*(5) = 17;
%e A125282 a(5) = 5^0*(1) + 4^1*(1) + 3^2*(2) + 2^3*(5) + 1^4*(17) = 80;
%e A125282 a(6) = 6^0*(1) + 5^1*(1) + 4^2*(2) + 3^3*(5) + 2^4*(17) + 1^5*(80) = 
               525.
%o A125282 (PARI) {a(n)=if(n==0,1,sum(k=0,n-1,(n-k)^k*a(k)))}
%Y A125282 Cf. A125281 (variant).
%Y A125282 Sequence in context: A020096 A054499 A001186 this_sequence A020125 A076322 
               A098540
%Y A125282 Adjacent sequences: A125279 A125280 A125281 this_sequence A125283 A125284 
               A125285
%K A125282 nonn
%O A125282 0,3
%A A125282 Paul D. Hanna (pauldhanna(AT)juno.com), Nov 29 2006