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 A208833 G.f.: 1+x = Sum_{n>=0} a(n) * x^n * Product_{k=1..n} (1 - k*x)/(1 + k*x). 1

%I

%S 1,1,2,10,86,1082,18202,386834,9990206,304821826,10757265314,

%T 431846459786,19460311559446,973722006221210,53610324625950938,

%U 3223029995174243506,210202324733850002846,14787932100812573072642,1116673488757504695366658,90116245915518156986943818

%N G.f.: 1+x = Sum_{n>=0} a(n) * x^n * Product_{k=1..n} (1 - k*x)/(1 + k*x).

%e G.f.: 1+x = 1 + 1*x*(1-x)/(1+x) + 2*x^2*(1-x)*(1-2*x)/((1+x)*(1+2*x)) + 10*x^3*(1-x)*(1-2*x)*(1-3*x)/((1+x)*(1+2*x)*(1+3*x)) + 86*x^4*(1-x)*(1-2*x)*(1-3*x)*(1-4*x)/((1+x)*(1+2*x)*(1+3*x)*(1+4*x)) +...

%o (PARI) {a(n)=if(n==0, 1, polcoeff(1+x-sum(k=0, n-1, a(k)*x^k*prod(j=1, k, (1-j*x)/(1+j*x+x*O(x^n)))), n))}

%o for(n=0,25,print1(a(n),", "))

%Y Cf. A208832.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Mar 01 2012

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Last modified May 27 01:53 EDT 2022. Contains 354092 sequences. (Running on oeis4.)