A209298 E.g.f.: Product_{n>=1} (cos(x^n/n) + sin(x^n/n)).

1, 1, 0, 4, 6, 30, 348, 1580, 12516, 114884, 1375776, 12239280, 160067160, 1966619512, 28104385008, 428735710000, 6769181533968, 110402248461840, 2070626881211136, 38342125010072384, 764180537501729376, 16185744192232110560, 354756690964676468160

Offset

0,4

Comments

Compare to: Product_{n>=1} (cosh(x^n/n) + sinh(x^n/n)) = 1/(1-x).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Example

E.g.f.: A(x) = 1 + x + 4*x^3/3! + 6*x^4/4! + 30*x^5/5! + 348*x^6/6! +...
where A(x) = (cos(x)+sin(x)) * (cos(x^2/2)+sin(x^2/2)) * (cos(x^3/3)+sin(x^3/3)) * (cos(x^4/4)+sin(x^4/4)) * (cos(x^5/5)+sin(x^5/5)) *...
What is the limit a(n)/n! = ?
Example:
a(1000)/1000! = 0.2942615679517020268...
a(2000)/2000! = 0.2939735835938621667...
a(3000)/3000! = 0.2938768494981674721...
a(4000)/4000! = 0.2938283311328618257...
a(5000)/5000! = 0.2937991678075013564...
a(6000)/6000! = 0.2937797033327244435...

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(Cos[x^n/n] + Sin[x^n/n]), {n, 1, 200}], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jan 03 2018 *)

Prog

(PARI) {a(n)=n!*polcoeff(prod(k=1, n, cos(x^k/k +x*O(x^n))+sin(x^k/k +x*O(x^n))), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A209299.

Sequence in context: A154667 A093121 A248048 * A075590 A088255 A192083

Adjacent sequences: A209295 A209296 A209297 * A209299 A209300 A209301

Keyword

nonn

Author

Paul D. Hanna, Jan 17 2013

Status

approved