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!)
A142704 A generalized factorial level recursion of a Padovan type: a(n) = b(n)*(a(n-2) + a(n-3)) with b(n) = b(n-1) + k and k=2. 1
0, 1, 1, 6, 16, 70, 264, 1204, 5344, 26424, 130960, 698896, 3777216, 21576256, 125331136, 760604160, 4701036544, 30121800064, 196619065344, 1323267791104, 9069634616320, 63835247970816, 457287705926656 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

FORMULA

a(n) = b(n)*(a(n-2) + a(n-3)) with b(n) = b(n-1) + k and k = 2.

a(n) = 2*n*(a(n-2) + a(n-3)) with a(0) = 0, a(1) = a(2) = 1 [Johannes W. Meijer, Jul 27 2011]

E.g.f.: Pi/(4*sqrt(2))*exp(x^2/2)*x*sqrt(1+x)*(BesselI(-1/4,1/2*(1+x)^2)*(2*BesselI(-3/4,1/2)-BesselI(1/4,1/2))+BesselI(1/4,1/2*(1+x)^2)*(BesselI(-1/4,1/2)-2*BesselI(3/4,1/2))). - Vaclav Kotesovec, Dec 28 2012

a(n) ~ sqrt(Pi)/8 * (2*BesselI(-3/4,1/2) - 2*BesselI(3/4,1/2) + BesselI(-1/4,1/2) - BesselI(1/4,1/2)) * 2^(n/2-1/4)*exp(sqrt(n)/sqrt(2)-n/2+3/8)*n^(n/2+1/4) * (1-47/(48*sqrt(2*n))). - Vaclav Kotesovec, Dec 28 2012

MAPLE

A142704 := proc(n) option remember: if n=0 then 0 elif n=1 then 1 elif n =2 then 1 elif n>=3 then 2*n*(procname(n-2) + procname(n-3)) fi: end: seq(A142704(n), n=0..22); [Johannes W. Meijer, Jul 27 2011]

MATHEMATICA

Clear[a, b, n, k]; k = 2; b[0] = 0; b[n_] := b[n] = b[n - 1] + k; a[0] = 0; a[1] = 1; a[2] = 2; a[n_] := a[n] = b[n]*(a[n - 2] + a[n - 3]); Table[a[n], {n, 0, 22}]

FullSimplify[CoefficientList[Series[Pi/(4*Sqrt[2])*E^(x^2/2)*x *Sqrt[1+x] *(BesselI[-1/4, 1/2*(1+x)^2]*(2*BesselI[-3/4, 1/2] - BesselI[1/4, 1/2]) + BesselI[1/4, 1/2*(1+x)^2]*(BesselI[-1/4, 1/2] - 2*BesselI[3/4, 1/2])), {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Dec 28 2012 *)

CROSSREFS

Cf. A171386 (k=0), A108189 (k=1), A002467 (Game of Mousetrap), A000931 (Padovan).

Sequence in context: A120795 A118640 A277747 * A083885 A211954 A230942

Adjacent sequences:  A142701 A142702 A142703 * A142705 A142706 A142707

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula and Gary W. Adamson, Sep 24 2008

EXTENSIONS

Edited and information added by Johannes W. Meijer, Jul 27 2011

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 3 21:14 EST 2016. Contains 278745 sequences.