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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A261611 Expansion of Product_{k>=0} (1 + x^(4*k+1))/(1 - x^(4*k+1)). 7
1, 2, 2, 2, 2, 4, 6, 6, 6, 8, 12, 14, 14, 16, 22, 28, 30, 32, 40, 50, 56, 60, 70, 86, 98, 106, 120, 144, 166, 180, 200, 234, 270, 296, 324, 372, 428, 472, 514, 580, 664, 736, 800, 890, 1010, 1124, 1222, 1346, 1514, 1684, 1834, 2008, 2240, 2488, 2712, 2956 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

In general, if a > 0, b > 0, GCD(a,b) = 1 and g.f. = Product_{k>=0} (1 + x^(a*k+b))/(1 - x^(a*k+b)), then a(n) ~ Gamma(b/a) * a^(b/(2*a) - 1/2) * Pi^(b/a - 1) * exp(Pi*sqrt(n/a)) / (2^(2*b/a + 1) * n^(b/(2*a) + 1/2)).

LINKS

Table of n, a(n) for n=0..55.

FORMULA

a(n) ~ exp(Pi*sqrt(n)/2) * Gamma(1/4) / (2^(9/4) * Pi^(3/4) * n^(5/8)).

MATHEMATICA

nmax = 60; CoefficientList[Series[Product[(1 + x^(4*k+1))/(1 - x^(4*k+1)), {k, 0, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A015128, A080054, A261610.

Sequence in context: A045812 A064877 A008363 * A097198 A126663 A032600

Adjacent sequences:  A261608 A261609 A261610 * A261612 A261613 A261614

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Aug 26 2015

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 November 13 15:41 EST 2019. Contains 329106 sequences. (Running on oeis4.)