login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A266971 Expansion of Product_{k>=1} 1 / (1 + k*x^k)^k. 7
1, -1, -3, -6, 2, 9, 41, 46, 91, -110, -210, -713, -574, -1152, 792, 1066, 9317, 8553, 21302, 745, 8051, -82940, -76750, -276022, -82369, -404100, 381095, -38110, 2427272, 1126260, 6527840, 198507, 9754305, -14320206, 2879362, -60271740, -5154261, -143468194 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For n > 36 is a(n) > 0 if n is even and a(n) < 0 if n is odd.

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = n, g(n) = -n. - Seiichi Manyama, Nov 18 2017

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..6224 (terms 0..1000 from Vaclav Kotesovec)

FORMULA

a(n) ~ c * (-1)^n * n^2 * 3^(n/3), where

c = 50.5838262902886367070621... if mod(n,3)=0,

c = 50.5827771239052189170531... if mod(n,3)=1,

c = 50.5832885870455104598393... if mod(n,3)=2.

a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} b(k)*a(n-k) where b(n) = Sum_{d|n} d^2*(-d)^(n/d). - Seiichi Manyama, Nov 18 2017

MATHEMATICA

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

PROG

(PARI) N=66; x='x+O('x^N); Vec(1/prod(k=1, N, (1+k*x^k)^k)) \\ Seiichi Manyama, Nov 18 2017

(Ruby)

def s(f_ary, g_ary, n)

  s = 0

  (1..n).each{|i| s += i * f_ary[i] * g_ary[i] ** (n / i) if n % i == 0}

  s

end

def A(f_ary, g_ary, n)

  ary = [1]

  a = [0] + (1..n).map{|i| s(f_ary, g_ary, i)}

  (1..n).each{|i| ary << (1..i).inject(0){|s, j| s + a[j] * ary[-j]} / i}

  ary

end

def A266971(n)

  A((0..n).to_a, (0..n).map{|i| -i}, n)

end

p A266971(50) # Seiichi Manyama, Nov 18 2017

CROSSREFS

Cf. A022629, A022693, A266891, A266941, A266964.

Sequence in context: A205001 A154204 A309609 * A257106 A210187 A210189

Adjacent sequences:  A266968 A266969 A266970 * A266972 A266973 A266974

KEYWORD

sign

AUTHOR

Vaclav Kotesovec, Jan 07 2016

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 1 01:37 EST 2021. Contains 349426 sequences. (Running on oeis4.)