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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A159478 a(n) = 2^(n^2+n) * C(1/2^n, n). 5
1, 2, -6, 140, -14570, 6283452, -11049839724, 78893138035608, -2282580118745565210, 267227101453296251927660, -126415241162450125116966673796, 241332381844862786094865482962203112, -1857025703922208959523779453799872508349700 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Sum_{n>=0} C(1/2^n, n) = 1.4306345243611686570661803375590... (A139823).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..57

FORMULA

G.f.: Sum_{n>=0} a(n)*x^n/2^(n^2+n) = Sum_{n>=0} log(1 + x/2^n)^n/n!.

a(n) = [x^n] (1 + 2^(n+1)*x)^(1/2^n).

a(n) ~ -(-1)^n * 2^(n^2)/n. - Vaclav Kotesovec, Jun 29 2018

EXAMPLE

G.f.: A(x) = 1 +2*x/2^2 -6*x^2/2^6 +140*x^3/2^12 -14570*x^4/2^20 +...

A(x) = 1 + log(1+x/2) + log(1+x/4)^2/2! + log(1+x/8)^3/3! +...

Illustrate a(n) = [x^n] (1 + 2^(n+1)*x)^(1/2^n):

(1+4*x)^(1/2) = 1 + (2)*x - 2*x^2 + 4*x^3 - 10*x^4 +...

(1+8*x)^(1/4) = 1 + 2*x - (6)*x^2 + 28*x^3 - 154*x^4 +...

(1+16*x)^(1/8) = 1 + 2*x - 14*x^2 + (140)*x^3 - 1610*x^4 +...

(1+32*x)^(1/16) = 1 + 2*x - 30*x^2 + 620*x^3 - (14570)*x^4 +...

(1+64*x)^(1/32) = 1 + 2*x - 62*x^2 + 2604*x^3 - 123690*x^4 + (6283452)*x^5 +...

MATHEMATICA

Table[2^(n^2 + n)*Binomial[1/2^n, n], {n, 0, 25}] (* G. C. Greubel, Jun 12 2018 *)

PROG

(PARI) a(n)=2^(n^2+n)*binomial(1/2^n, n)

(MAGMA) SetDefaultRealField(RealField(250)); [Round(2^(n + n^2)*Gamma(1 + 1/2^n)/(Gamma(n+1)*Gamma(1 + 1/2^n - n))): n in [0..25]]; // G. C. Greubel, Jun 12 2018

CROSSREFS

Cf. A139823.

Sequence in context: A254223 A206849 A090907 * A047937 A027731 A280821

Adjacent sequences:  A159475 A159476 A159477 * A159479 A159480 A159481

KEYWORD

sign

AUTHOR

Paul D. Hanna, Apr 19 2009

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 September 16 12:28 EDT 2019. Contains 327098 sequences. (Running on oeis4.)