cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A303345 Expansion of Product_{k>=1} ((1 - 2*x^k)/(1 + 2*x^k))^(1/2).

Original entry on oeis.org

1, -2, 0, -2, 6, -6, 12, -22, 48, -94, 160, -318, 622, -1210, 2268, -4482, 8678, -16998, 32632, -64366, 124674, -245866, 476108, -940866, 1829148, -3617066, 7040112, -13937530, 27186810, -53857062, 105196572, -208546726, 407944704, -809175966, 1584713040
Offset: 0

Views

Author

Seiichi Manyama, Apr 22 2018

Keywords

Links

Crossrefs

Cf. A303306, A303346, A303439.
Expansion of Product_{k>=1} ((1 - 2^b*x^k)/(1 + 2^b*x^k))^(1/(2^b)): A002448 (b=0), this sequence (b=1), A303387 (b=2), A303396 (b=3).

Programs

  • Maple
    seq(coeff(series(mul(((1-2*x^k)/(1+2*x^k))^(1/2), k = 1..n), x, n+1), x, n), n=0..40); # Muniru A Asiru, Apr 22 2018
  • PARI
    N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1-2*x^k)/(1+2*x^k))^(1/2)))

Formula

a(n) ~ c * (-2)^n / sqrt(Pi*n), where c = (QPochhammer[-1, -1/2] / QPochhammer[-1/2])^(1/2) = 0.96924509195711964009315.... - Vaclav Kotesovec, Apr 25 2018

A303387 Expansion of Product_{k>=1} ((1 - 4*x^k)/(1 + 4*x^k))^(1/4).

Original entry on oeis.org

1, -2, 0, -10, 22, -102, 244, -1270, 3360, -16886, 46160, -230670, 656550, -3238250, 9474684, -46289530, 138590342, -671116710, 2047182480, -9837322110, 30482926482, -145474988978, 456854466860, -2166890174370, 6884188144964, -32471461699594
Offset: 0

Views

Author

Seiichi Manyama, Apr 23 2018

Keywords

Links

Crossrefs

Expansion of Product_{k>=1} ((1 - 2^b*x^k)/(1 + 2^b*x^k))^(1/(2^b)): A002448 (b=0), A303345 (b=1), this sequence (b=2), A303396 (b=3).
Cf. A303360, A303402.

Programs

  • Maple
    seq(coeff(series(mul(((1-4*x^k)/(1+4*x^k))^(1/4), k = 1..n), x, n+1), x, n), n=0..25); # Muniru A Asiru, Apr 23 2018
  • PARI
    N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1-4*x^k)/(1+4*x^k))^(1/4)))

Formula

a(n) ~ c * (-4)^n / n^(3/4), where c = (QPochhammer[-1, -1/4] / QPochhammer[-1/4])^(1/4) / Gamma(1/4) = 0.29599817925108933574246285.... - Vaclav Kotesovec, Apr 25 2018

A303439 Expansion of Product_{k>=1} ((1 - 2^k*x^k)/(1 + 2^k*x^k))^(1/2^k).

Original entry on oeis.org

1, -2, 0, -2, 6, -6, 4, -6, 48, -118, 96, -78, 470, -810, 396, -3050, 11062, -12678, 7072, -21454, 80034, -201490, 218940, -200658, 1536724, -3268842, 2079312, -7013266, 23140282, -28227510, 24133668, -56293910, 288065712, -704485126, 629862288, -1176210654
Offset: 0

Views

Author

Seiichi Manyama, Apr 24 2018

Keywords

Links

Crossrefs

Cf. A303345, A303387, A303396, A303438.

Programs

  • Mathematica
    nmax = 30; CoefficientList[Series[Exp[Sum[(1 - (-1)^j) / (j*(1 - 1/(2^(j-1)*x^j))), {j, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 25 2018 *)
  • PARI
    N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1-2^k*x^k)/(1+2^k*x^k))^(1/2^k)))
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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