A194457 E.g.f.: Sum_{n>=0} 2^(-n*(n+1)/2!) * Product_{k=0..n} tanh(2^k*x).

1, 2, 4, -16, -704, -17728, -337616, 11402624, 3549329536, 595083636992, 71290751812864, -14356598757876736, -25888783158323201024, -24314339173695033407488, -15893228305971746577453056, 17044727383475526594464251904, 160878265780790778493935871983616

Offset

1,2

Comments

Signs of terms are of period 8: [+,+,+,-,-,-,-,+].

Links

Table of n, a(n) for n=1..17.

Formula

E.g.f.: Sum_{n>=0} sinh(x)^(n+1) * Product_{k=0..n} cosh(2^k*x)^(n-1-k).

Example

E.g.f.: A(x) = x + 2*x^2/2! + 4*x^3/3! - 16*x^4/4! - 704*x^5/5! +...
where
A(x) = tanh(x) + tanh(x)*tanh(2*x)/2 + tanh(x)*tanh(2*x)*tanh(4*x)/2^3 + tanh(x)*tanh(2*x)*tanh(4*x)*tanh(8*x)/2^6 +...
A(x) = sinh(x)/cosh(x) + sinh(x)^2/cosh(2*x) + sinh(x)^3*cosh(x)/cosh(4*x) + sinh(x)^4*cosh(x)^2*cosh(2*x)/cosh(8*x) + sinh(x)^5*cosh(x)^3*cosh(2*x)^2*cosh(4*x)/cosh(16*x) + sinh(x)^6*cosh(x)^4*cosh(2*x)^3*cosh(4*x)^2*cosh(8*x)/cosh(32*x) +...

Prog

(PARI) {a(n)=local(A=sum(m=0, n, 2^(-m*(m+1)/2!)*prod(k=0, m, tanh(2^k*x+x*O(x^n))))); n!*polcoeff(A, n)}
(PARI) {a(n)=local(X=x+x*O(x^n), A=sum(m=0, n, sinh(X)^(m+1)*prod(k=0, m, cosh(2^k*X)^(m-1-k)))); n!*polcoeff(A, n)}

Crossrefs

Cf. A194456, A194026, A194027.

Sequence in context: A001146 A114641 A152690 * A371717 A001128 A280890

Adjacent sequences: A194454 A194455 A194456 * A194458 A194459 A194460

Keyword

sign

Author

Paul D. Hanna, Aug 24 2011

Status

approved