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A218683 E.g.f. satisfies: A(x) = Sum_{n>=0} n^n * x^n/n! * A(n*x). 2

%I

%S 1,1,6,69,1432,52065,3202176,324172597,53099867136,13888279032129,

%T 5736880791449920,3710252136325373661,3729910949734728414624,

%U 5792791811385586637686849,13826260704559808415109532256,50488064853691920270244556417445

%N E.g.f. satisfies: A(x) = Sum_{n>=0} n^n * x^n/n! * A(n*x).

%F a(n) = Sum_{k=0..n-1} binomial(n,k) * (n-k)^n * a(k) for n>0 with a(0)=1.

%e E.g.f.: A(x) = 1 + x + 6*x^2/2! + 69*x^3/3! + 1432*x^4/4! + 52065*x^5/5! +...

%e where

%e A(x) = 1 + x*A(x) + 2^2*x^2*A(2*x)/2! + 3^3*x^3*A(3*x)/3! + 4^4*x^4*A(4*x)/4! +...

%e which leads to the recurrence illustrated by:

%e a(1) = 1*1^1*(1) = 1;

%e a(2) = 1*2^2*(1) + 2*1^2*(1) = 6;

%e a(3) = 1*3^3*(1) + 3*2^3*(1) + 3*1^3*(6) = 69;

%e a(4) = 1*4^4*(1) + 4*3^4*(1) + 6*2^4*(6) + 4*1^4*(69) = 1432;

%e a(5) = 1*5^5*(1) + 5*4^5*(1) + 10*3^5*(6) + 10*2^5*(69) + 5*1^5*(1432) = 52065.

%o (PARI) {a(n)=local(A=1);for(i=1,n,A=sum(k=0,n,k^k*x^k/k!*subst(A,x,k*x)+x*O(x^n)));n!*polcoeff(A,n)}

%o for(n=0,20,print1(a(n),", "))

%o (PARI) {a(n)=if(n==0, 1, sum(k=0, n-1, binomial(n, k)*(n-k)^n*a(k)))}

%o for(n=0,20,print1(a(n),", "))

%Y Cf. A125281, A218682.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 05 2012

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Last modified September 22 03:20 EDT 2021. Contains 347605 sequences. (Running on oeis4.)