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%I #7 Mar 30 2012 18:37:26
%S 1,1,4,32,404,7136,164088,4683680,160473988,6437653568,296657482888,
%T 15467576203136,901391710293832,58122426582341120,4111838048797360624,
%U 316858691136196764672,26432968974665127895908,2374343115004631725352960
%N G.f.: 1 = Sum_{n>=0} a(n) * x^n*(1 - (n+1)*x)^(n+1).
%C Compare to a g.f. for A000272:
%C 1 = Sum_{n>=0} (n+1)^(n-1) * x^n/(1 + (n+1)*x)^(n+1).
%F a(n) = Sum_{k=1..[(n+1)/2]} -(-1)^k * C(n+1-k,k) * (n+1-k)^k * a(n-k).
%e G.f.: 1 = (1-x) + x*(1-2*x)^2 + 4*x^2*(1-3*x)^3 + 32*x^3*(1-4*x)^4 + 404*x^4*(1-5*x)^5 + 7136*x^5*(1-6*x)^6 +...
%e Compare to a g.f. for A000272:
%e 1 = 1/(1+x) + x/(1+2*x)^2 + 3*x^2/(1+3*x)^3 + 4^2*x^3/(1+4*x)^4 + 5^3*x^4/(1+5*x)^5 + 6^4*x^5/(1+6*x)^6 +...
%o (PARI) {a(n)=polcoeff(1-sum(k=0, n-1, a(k)*x^k*(1-(k+1)*x+x*O(x^n))^(k+1)), n)}
%o (PARI) {a(n)=if(n==0,1,-sum(k=1,(n+1)\2,(-1)^k*binomial(n+1-k,k)*a(n-k)*(n+1-k)^k))}
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 02 2011
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