A172388 a(n) = Sum_{k=0..n} (-1)^k*C(n,k)*2^(k*(n-k)).
1, 0, -2, 0, 34, 0, -2942, 0, 1144834, 0, -1906714622, 0, 13264071114754, 0, -380188784001777662, 0, 44530311225683389448194, 0, -21199108233888497863938801662, 0, 40869840581497696551494454452682754
Offset: 0
Keywords
Examples
O.g.f.: A(x) = 1 - 2*x^2 + 34*x^4 - 2942*x^6 + 1144834*x^8 +... 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.g.f.: E(x) = 1 - 2*x^2/2! + 34*x^4/4! - 2942*x^6/6! + 1144834*x^8/8! +... 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! +...
Programs
-
PARI
{a(n)=sum(k=0,n,(-1)^k*binomial(n,k)*2^(k*(n-k)))} -
PARI
{a(n)=polcoeff(sum(k=0, n, x^k/(1+2^k*x +x*O(x^n))^(k+1)), n)} -
PARI
{a(n)=n!*polcoeff(sum(k=0, n, exp(-2^k*x +x*O(x^n))*x^k/k!), n)}
Formula
O.g.f.: A(x) = Sum_{n>=0} x^n/(1+2^n*x)^(n+1).
E.g.f.: E(x) = Sum_{n>=0} exp(-2^n*x)*x^n/n!.