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!)
A301554 Expansion of Product_{k>=1} ((1 + x^k)/(1 - x^k))^(sigma_0(k)). 20
1, 2, 6, 14, 32, 66, 138, 266, 512, 948, 1730, 3074, 5408, 9306, 15854, 26594, 44150, 72378, 117620, 189074, 301516, 476518, 747514, 1163470, 1798920, 2762040, 4215194, 6393196, 9642596, 14462518, 21581386, 32040562, 47345342, 69635866, 101974722, 148692638 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Convolution of A006171 and A107742.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

FORMULA

G.f.: Product_{i>=1, j>=1} (1 + x^(i*j))/(1 - x^(i*j)). - Ilya Gutkovskiy, May 23 2018

Conjecture: log(a(n)) ~ Pi * sqrt(n*log(n)/2). - Vaclav Kotesovec, Sep 03 2018

MAPLE

with(numtheory): seq(coeff(series(mul(((1+x^k)/(1-x^k))^sigma[0](k), k=1..n), x, n+1), x, n), n = 0 .. 35); # Muniru A Asiru, Oct 29 2018

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[((1+x^k)/(1-x^k))^DivisorSigma[0, k], {k, 1, nmax}], {x, 0, nmax}], x]

PROG

(PARI) m=50; x='x+O('x^m); Vec(prod(k=1, m, prod(j=1, m+2, (1+x^(j*k))/(1-x^(j*k)) ))) \\ G. C. Greubel, Oct 29 2018

(MAGMA) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[(&*[(1 + x^(j*k))/(1-x^(j*k)): j in [1..(m+2)]]): k in [1..(m+2)]]))); // G. C. Greubel, Oct 29 2018

CROSSREFS

Cf. A000005, A006171, A107742, A320237.

Sequence in context: A327049 A035592 A327050 * A217941 A232434 A096238

Adjacent sequences:  A301551 A301552 A301553 * A301555 A301556 A301557

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 23 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 11 23:44 EST 2019. Contains 329945 sequences. (Running on oeis4.)