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 A205803 E.g.f.: -log( Sum_{n>=0} (-x)^(n*(n+1)/2) / (n*(n+1)/2)! ). 3

%I

%S 1,1,3,10,44,249,1693,13384,120932,1229759,13894429,172677450,

%T 2341111850,34385290940,543885462121,9217332132024,166621796893824,

%U 3200275345024464,65082833538054240,1397097303096855578,31569176387677926733,749012642530028865010

%N E.g.f.: -log( Sum_{n>=0} (-x)^(n*(n+1)/2) / (n*(n+1)/2)! ).

%e E.g.f.: A(x) = x + x^2/2! + 3*x^3/3! + 10*x^4/4! + 44*x^5/5! + 249*x^6/6! +...

%e where

%e exp(-A(x)) = 1 - x - x^3/3! + x^6/6! + x^10/10! - x^15/15! - x^21/21! +...

%o (PARI) {a(n)=n!*polcoeff(-log(sum(m=0, sqrtint(2*n+1), (-x)^(m*(m+1)/2)/(m*(m+1)/2)!+x*O(x^n))), n)}

%Y Cf. A205804.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Jan 31 2012

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Last modified August 3 13:22 EDT 2021. Contains 346438 sequences. (Running on oeis4.)