cp's OEIS Frontend

A172388 a(n) = Sum_{k=0..n} (-1)^k*C(n,k)*2^(k*(n-k)).

%I A172388 #2 Mar 30 2012 18:37:20
%S A172388 1,0,-2,0,34,0,-2942,0,1144834,0,-1906714622,0,13264071114754,0,
%T A172388 -380188784001777662,0,44530311225683389448194,0,
%U A172388 -21199108233888497863938801662,0,40869840581497696551494454452682754
%N A172388 a(n) = Sum_{k=0..n} (-1)^k*C(n,k)*2^(k*(n-k)).
%F A172388 O.g.f.: A(x) = Sum_{n>=0} x^n/(1+2^n*x)^(n+1).
%F A172388 E.g.f.: E(x) = Sum_{n>=0} exp(-2^n*x)*x^n/n!.
%e A172388 O.g.f.: A(x) = 1 - 2*x^2 + 34*x^4 - 2942*x^6 + 1144834*x^8 +...
%e A172388 A(x) = 1/(1+x) + x/(1+2*x)^2 + x^2/(1+2^2*x)^3 + x^3/(1+2^3*x)^4 +...+ x^n/(1+2^n*x)^(n+1) +...
%e A172388 E.g.f.: E(x) = 1 - 2*x^2/2! + 34*x^4/4! - 2942*x^6/6! + 1144834*x^8/8! +...
%e A172388 E(x) = exp(-x) + exp(-2*x)*x + exp(-2^2*x)*x^2/2! + exp(-2^3*x)*x^3/3! +...+ exp(-2^n*x)*x^n/n! +...
%o A172388 (PARI) {a(n)=sum(k=0,n,(-1)^k*binomial(n,k)*2^(k*(n-k)))}
%o A172388 (PARI) {a(n)=polcoeff(sum(k=0, n, x^k/(1+2^k*x +x*O(x^n))^(k+1)), n)}
%o A172388 (PARI) {a(n)=n!*polcoeff(sum(k=0, n, exp(-2^k*x +x*O(x^n))*x^k/k!), n)}
%Y A172388 Cf. variants: A172389, A047863.
%K A172388 sign
%O A172388 0,3
%A A172388 _Paul D. Hanna_, Feb 03 2010