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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A261568 Expansion of Product_{k>=1} (1 + 4*x^k). 8
1, 4, 4, 20, 20, 36, 100, 116, 180, 260, 580, 660, 1044, 1380, 2020, 3444, 4340, 6020, 8260, 11220, 14740, 23140, 28196, 38900, 50420, 67780, 85956, 114900, 157140, 197860, 257060, 331060, 423540, 540100, 687620, 864084, 1145300, 1406500, 1789860, 2231860 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

a(n) ~ c^(1/4) * exp(2*sqrt(c*n)) / (2*sqrt(5*Pi)*n^(3/4)), where c = Pi^2/6 + 2*log(2)^2 + polylog(2, -1/4) = 2.36993979699836583198553742535032304875... . - Vaclav Kotesovec, Jan 04 2016

G.f.: Sum_{i>=0} 4^i*x^(i*(i+1)/2)/Product_{j=1..i} (1 - x^j). - Ilya Gutkovskiy, Apr 12 2018

MAPLE

b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,

      `if`(n=0, 1, b(n, i-1)+`if`(i>n, 0, 4*b(n-i, i-1))))

    end:

a:= n-> b(n$2):

seq(a(n), n=0..60);  # Alois P. Heinz, Aug 24 2015

MATHEMATICA

nmax = 40; CoefficientList[Series[Product[1 + 4*x^k, {k, 1, nmax}], {x, 0, nmax}], x]

nmax = 40; CoefficientList[Series[Exp[Sum[(-1)^(k+1)*4^k/k*x^k/(1-x^k), {k, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 25 2015 *)

(QPochhammer[-4, x]/5 + O[x]^58)[[3]] (* Vladimir Reshetnikov, Nov 20 2015 *)

CROSSREFS

Cf. A000009, A032302, A032308, A261569.

Sequence in context: A271810 A264528 A035413 * A087213 A117857 A165559

Adjacent sequences:  A261565 A261566 A261567 * A261569 A261570 A261571

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Aug 24 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 15 01:25 EST 2019. Contains 329143 sequences. (Running on oeis4.)