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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A318570 Expansion of Product_{k>=1} ((1 - x)^k + x^k)/((1 - x)^k - x^k). 3
1, 2, 6, 18, 52, 146, 402, 1090, 2916, 7708, 20160, 52236, 134222, 342304, 867024, 2182384, 5461696, 13595918, 33677550, 83036878, 203859820, 498470998, 1214230586, 2947204870, 7129403128, 17191258642, 41328057106, 99067295658, 236822823336, 564650823162, 1342921372126 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

First differences of the binomial transform of A015128.

Convolution of A129519 and A218482.

LINKS

Table of n, a(n) for n=0..30.

N. J. A. Sloane, Transforms

FORMULA

G.f.: 1/theta_4(x/(1 - x)), where theta_4() is the Jacobi theta function.

G.f.: exp(Sum_{k>=1} (sigma(2*k) - sigma(k))*x^k/(k*(1 - x)^k)).

a(n) ~ 2^(n-3) * exp(Pi*sqrt(n/2) + Pi^2/16) / n. - Vaclav Kotesovec, Oct 15 2018

MAPLE

a:=series(mul(((1-x)^k+x^k)/((1-x)^k-x^k), k=1..100), x=0, 31): seq(coeff(a, x, n), n=0..30); # Paolo P. Lava, Apr 02 2019

MATHEMATICA

nmax = 30; CoefficientList[Series[Product[((1 - x)^k + x^k)/((1 - x)^k - x^k), {k, 1, nmax}], {x, 0, nmax}], x]

nmax = 30; CoefficientList[Series[1/EllipticTheta[4, 0, x/(1 - x)], {x, 0, nmax}], x]

nmax = 30; CoefficientList[Series[Exp[Sum[(DivisorSigma[1, 2 k] - DivisorSigma[1, k]) x^k/(k (1 - x)^k), {k, 1, nmax}]], {x, 0, nmax}], x]

CROSSREFS

Cf. A000203, A015128, A129519, A218482, A266497.

Sequence in context: A018249 A245285 A128104 * A027059 A078484 A156989

Adjacent sequences:  A318567 A318568 A318569 * A318571 A318572 A318573

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Oct 15 2018

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 December 9 23:00 EST 2019. Contains 329880 sequences. (Running on oeis4.)