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.

A269153 Expansion of Product_{k>=1} ((1 - k*x^k) / (1 - 2*x^k)).

Original entry on oeis.org

1, 1, 2, 3, 5, 9, 15, 33, 62, 130, 264, 554, 1081, 2237, 4483, 8952, 17933, 35921, 71755, 143502, 286713, 573198, 1146540, 2292277, 4584087, 9166802, 18334880, 36668210, 73336840, 146672469, 293348402, 586695560, 1173398119, 2346805311, 4693617598, 9387229673
Offset: 0

Views

Author

Vaclav Kotesovec, Feb 20 2016

Keywords

Crossrefs

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) = 0.27320499481666294779155052256744055231134605935215258251663905...

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

Crossrefs

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

Crossrefs

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.