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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A032109 "BIJ" (reversible, indistinct, labeled) transform of 1,1,1,1... 3
1, 1, 2, 7, 38, 271, 2342, 23647, 272918, 3543631, 51123782, 811316287, 14045783798, 263429174191, 5320671485222, 115141595488927, 2657827340990678, 65185383514567951, 1692767331628422662 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Starting (1, 2, 7, 38, 271,...) = A008292 * [1, 1, 2, 4, 8,...]. [Gary W. Adamson, Dec 25 2008]

The inverse binomial transform is 1, 0, 1, 3, 19, 135, 1171, 11823, 136459,.. , see A091346. - R. J. Mathar, Oct 17 2012

Stirling transform of A001710. - Anton Zakharov, Aug 06 2016

LINKS

R. J. Mathar, Table of n, a(n) for n = 0..100

C. G. Bower, Transforms (2)

FORMULA

E.g.f.: (e^(2*x)-2*e^x-1)/(2*e^x-4).

a(n) = (A000670(n)+1)/2. - Vladeta Jovovic, Apr 13 2003

a(n) ~ sqrt(Pi/2)*n^(n+1/2)/(2*log(2)^(n+1)*exp(n)). - Ilya Gutkovskiy, Aug 06 2016

MAPLE

A032109 := proc(n)

    (A000670(n)+1)/2 ;

end proc: # R. J. Mathar, Oct 17 2012

a := n -> (polylog(-n, 1/2)+`if`(n=0, 3, 2))/4:

seq(round(evalf(a(n), 32)), n=0..18); # Peter Luschny, Nov 03 2015

MATHEMATICA

Table[(PolyLog[-n, 1/2] + 2 + KroneckerDelta[n])/4, {n, 0, 20}] (* Vladimir Reshetnikov, Nov 02 2015 *)

PROG

(PARI) a(n)=if(n<0, 0, n!*polcoeff(subst((1-y^2/2)/(1-y), y, exp(x+x*O(x^n))-1), n))

(PARI) list(n)=my(v=Vec(subst((1-y^2/2)/(1-y), y, exp(x+x*O(x^n))-1))); vector(n+1, i, v[i]*(i-1)!) \\ Charles R Greathouse IV, Oct 17 2012

CROSSREFS

A000629, A000670, A002050, A032109, A052856, A076726 are all more-or-less the same sequence. - N. J. A. Sloane, Jul 04 2012

A052856(n)=2*a(n), if n>0.

Cf. A008292, A001710.

Sequence in context: A256032 A209006 A168492 * A088792 A114160 A145159

Adjacent sequences:  A032106 A032107 A032108 * A032110 A032111 A032112

KEYWORD

nonn

AUTHOR

Christian G. Bower

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 7 19:05 EST 2016. Contains 278895 sequences.