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%I #13 Dec 25 2017 04:07:08
%S 1,1,2,10,92,1264,26138,753322,28451978,1385043022,84971475986,
%T 6393154081582,580295829204452,62818032904371952,8005929383232314294,
%U 1187186361565313907994,203034917331580351972520
%N G.f.: A(x) = Sum_{n>=0} x^n/[Sum_{k=0..n} C(n,k)^3*(-x)^k].
%C Compare the g.f. of this sequence to the identity:
%C (1-x)/(1-2*x) = Sum_{n>=0} x^n/[Sum_{k=0..n} C(n,k)*(-x)^k].
%H Robert Israel, <a href="/A181136/b181136.txt">Table of n, a(n) for n = 0..248</a>
%F G.f.: Sum_{n>=0} x^n/hypergeom([-n,-n,-n],[1,1],x). - _Robert Israel_, Dec 24 2017
%e G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 92*x^4 + 1264*x^5 +...
%e which equals the series:
%e A(x) = 1 + x/(1-x) + x^2/(1-2^3*x+x^2) + x^3/(1-3^3*x+3^3*x^2-x^3) + x^4/(1-4^3*x+6^3*x^2-4^3*x^3+x^4) + x^5/(1-5^3*x+10^3*x^2-10^3*x^3+5^3*x^4-x^5) +...
%p G:= add(x^n/hypergeom([-n,-n,-n],[1,1],x),n=0..50):
%p S:= series(G501,x,51):
%p seq(coeff(S,x,n),n=0..50); # _Robert Israel_, Dec 24 2017
%o (PARI) {a(n)=polcoeff(sum(m=0, n, x^m/sum(k=0, m, binomial(m, k)^3*(-x)^k+x*O(x^n))), n)}
%Y Cf. A178324.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 25 2011
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