login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A112940 INVERT transform (with offset) of quintuple factorials (A008546), where g.f. satisfies: A(x) = 1 + x*[d/dx x*A(x)^5]/A(x)^5. 10
1, 1, 5, 45, 605, 11045, 257005, 7288245, 243870205, 9401560645, 410141056205, 19966451812245, 1072718714991005, 63033317759267045, 4020725747388170605, 276661592017425909045, 20424931173615717011005 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

G.f. satisfies: A(x) = 1+x + 5*x^2*[d/dx A(x)]/A(x) (log derivative). G.f.: A(x) = 1+x +5*x^2/(1-9*x -5*2*4*x^2/(1-19*x -5*3*9*x^2/(1-29*x -5*4*13*x^2/(1-39*x -... -5*n*(5*n-6)*x^2/(1-(10*n-1)*x -...)))) (continued fraction). G.f.: A(x) = 1/(1-1*x/(1 -4*x/(1-5*x/(1 -9*x/(1-10*x/(1 -14*x/(1-15*x/(1 -...)))))))) (continued fraction).

G.f.: 1 + x/( Q(0) - x ) where Q(k) =  1 - x*(5*k+4)/(1 - x*(5*k+5)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Mar 20 2013

a(n) ~ (n-1)! * 5^(n-1) / (GAMMA(4/5) * n^(1/5)). - Vaclav Kotesovec, Feb 22 2014

EXAMPLE

A(x) = 1 + x + 5*x^2 + 45*x^3 + 605*x^4 + 11045*x^5 +...

1/A(x) = 1 - x - 4*x^2 - 36*x^3 - 504*x^4 -... -A008546(n)*x^(n+1) -...

MATHEMATICA

CoefficientList[Series[1/(1 + 1/5*ExpIntegralE[4/5, -1/(5*x)]/E^(1/(5*x))), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 22 2014 *)

PROG

(PARI) {a(n)=local(F=1+x+x*O(x^n)); for(i=1, n, F=1+x+5*x^2*deriv(F)/F); return(polcoeff(F, n, x))}

CROSSREFS

Cf. A008546, A112941 (log derivative); A112934, A112935, A112936, A112937, A112938, A112939, A112942, A112943.

Sequence in context: A090136 A090356 A201365 * A294332 A085356 A113382

Adjacent sequences:  A112937 A112938 A112939 * A112941 A112942 A112943

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 09 2005

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 21 12:12 EDT 2019. Contains 321369 sequences. (Running on oeis4.)