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.

A269144 Expansion of Product_{k>=1} ((1 + k*x^k) / (1 - 2*x^k)).

Original entry on oeis.org

1, 3, 10, 29, 77, 195, 475, 1115, 2546, 5706, 12528, 27106, 57893, 122299, 255995, 531816, 1097377, 2252151, 4600835, 9362334, 18990645, 38418370, 77548880, 156251955, 314363615, 631703790, 1268148900, 2543812090, 5099469848, 10217529291, 20464112218
Offset: 0

Views

Author

Vaclav Kotesovec, Feb 20 2016

Keywords

Comments

Convolution of A022629 and A070933.

Links

Crossrefs

Cf. A022629, A070933, A267004, A269153.

Programs

  • Mathematica
    nmax = 50; CoefficientList[Series[Product[(1+k*x^k)/(1-2*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * 2^n, where c = Product_{k>=1} (2^k + k)/(2^k - 1) = 19.14883592186082265751161402244824703642181055238186925199088...

A269154 Expansion of Product_{k>=1} (1 + k*x^k)/(1 + 2*x^k).

Original entry on oeis.org

1, -1, 2, -3, 9, -13, 31, -53, 118, -210, 452, -866, 1793, -3493, 7119, -13992, 28257, -56253, 113035, -225318, 451745, -901870, 1805976, -3609701, 7222075, -14439594, 28887060, -57763494, 115540784, -231066845, 462154358, -924282660, 1848598423, -3697142099
Offset: 0

Views

Author

Vaclav Kotesovec, Feb 20 2016

Keywords

Links

Crossrefs

Cf. A022629, A269144, A269153, A269155.

Programs

  • Mathematica
    nmax = 50; CoefficientList[Series[Product[(1+k*x^k)/(1+2*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * (-2)^n, where c = Product_{k>=1} ((-2)^k + k)/((-2)^k - 1) = 0.4304067090888734207149852218007129877370867778815471457548443780472...

A269155 Expansion of Product_{k>=1} (1 - k*x^k)/(1 + 2*x^k).

Original entry on oeis.org

1, -3, 2, -5, 17, -23, 43, -87, 178, -378, 700, -1402, 2837, -5651, 11295, -22592, 45397, -90587, 181187, -362566, 724949, -1449986, 2900068, -5801059, 11601675, -23204798, 46409816, -92817126, 185633688, -371270603, 742544062, -1485079884, 2970162411
Offset: 0

Views

Author

Vaclav Kotesovec, Feb 20 2016

Keywords

Links

Crossrefs

Cf. A269144, A269153, A269154.

Programs

  • Mathematica
    nmax = 50; CoefficientList[Series[Product[(1-k*x^k)/(1+2*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * (-2)^n, where c = Product_{k>=1} ((-2)^k - k)/((-2)^k - 1) = 0.691544539061740396647761051109300225267201237557458470928297389967...
Showing 1-3 of 3 results.

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