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A193198 G.f.: A(x) = Sum_{n>=0} x^n/(1 - 3^n*x)^n. 1

%I

%S 1,1,4,28,352,7696,296704,19845568,2325071872,472050401536,

%T 167325747134464,102717666720160768,109887628080679616512,

%U 203517277347030338768896,656102983404750860283019264,3660938644168893995628877692928

%N G.f.: A(x) = Sum_{n>=0} x^n/(1 - 3^n*x)^n.

%F a(n) = Sum_{k=0..n-1} C(n-1,k)*3^(k*(n-k)) for n>0 with a(0)=1.

%e G.f.: A(x) = 1 + x + 4*x^2 + 28*x^3 + 352*x^4 + 7696*x^5 +...

%e where:

%e A(x) = 1 + x/(1-3*x) + x^2/(1-9*x)^2 + x^3/(1-27*x)^3 + x^4/(1-81*x)^4 +...

%o (PARI) {a(n)=local(A=1);A=1+sum(m=1,n,x^m/(1-3^m*x +x*O(x^n))^m);polcoeff(A,n)}

%o (PARI) {a(n)=if(n==0,1,sum(k=0,n-1,binomial(n-1,k)*3^(k*(n-k))))}

%Y Cf. A000684, A193199.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jul 17 2011

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Last modified October 19 10:59 EDT 2021. Contains 348078 sequences. (Running on oeis4.)