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 1-5 of 5 results.

A318771 Expansion of Sum_{k>=0} x^(k^2) / Product_{j=1..k} (1 - x^j)^j.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 22, 25, 37, 47, 64, 81, 113, 140, 191, 243, 319, 408, 540, 677, 889, 1132, 1462, 1855, 2404, 3034, 3909, 4946, 6325, 7997, 10202, 12840, 16328, 20549, 25989, 32627, 41180, 51577, 64872, 81128, 101729, 127016, 158913, 197981, 247163, 307523, 383019
Offset: 0

Views

Author

Ilya Gutkovskiy, Sep 03 2018

Keywords

Crossrefs

Cf. A193197, A206100, A206138, A318770.

Programs

  • Maple
    a:=series(add(x^(k^2)/mul((1-x^j)^j,j=1..k),k=0..100),x=0,53): seq(coeff(a,x,n),n=0..52); # Paolo P. Lava, Apr 02 2019
  • Mathematica
    nmax = 52; CoefficientList[Series[Sum[x^k^2/Product[(1 - x^j)^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

A306706 Expansion of Sum_{k>=0} x^(k*(k+1)/2) / Product_{j=1..k} (1 + x^j)^j.

Original entry on oeis.org

1, 1, -1, 2, -2, 0, 1, 2, -4, -3, 7, 4, -4, -14, 6, 10, 12, -14, 0, -26, 3, 7, 60, 11, -27, -99, -26, 6, 126, 94, 58, -87, -180, -201, -46, 145, 282, 330, 142, -21, -515, -573, -716, -15, 423, 1519, 1128, 1197, -783, -1378, -3264, -1892, -1574, 2155, 2679, 6075, 3376, 3243
Offset: 0

Views

Author

Ilya Gutkovskiy, Mar 05 2019

Keywords

Crossrefs

Cf. A003406, A206138.

Programs

  • Mathematica
    nmax = 57; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 + x^j)^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

A306664 Expansion of Sum_{k>=0} x^(k*(k+1)) / Product_{j=1..k} (1 - x^j)^j.

Original entry on oeis.org

1, 0, 1, 1, 1, 1, 2, 2, 4, 4, 7, 7, 12, 12, 19, 22, 31, 37, 54, 63, 89, 111, 146, 184, 247, 301, 398, 501, 642, 804, 1042, 1293, 1663, 2082, 2648, 3321, 4229, 5268, 6691, 8370, 10553, 13168, 16595, 20659, 25929, 32253, 40321, 50092, 62489, 77418, 96340, 119266, 147998, 182927, 226609
Offset: 0

Views

Author

Ilya Gutkovskiy, Mar 04 2019

Keywords

Crossrefs

Cf. A003106, A206100, A206138.

Programs

  • Mathematica
    nmax = 54; CoefficientList[Series[Sum[x^(k (k + 1))/Product[(1 - x^j)^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

A306665 Expansion of Sum_{k>=0} k! * x^(k*(k+1)/2) / Product_{j=1..k} (1 - x^j)^j.

Original entry on oeis.org

1, 1, 1, 3, 3, 7, 13, 19, 31, 57, 99, 145, 253, 391, 661, 1071, 1647, 2617, 4189, 6439, 10183, 15999, 24195, 37537, 57553, 87925, 132841, 202899, 306147, 458827, 688501, 1030147, 1533535, 2280549, 3370947, 4986265, 7354573, 10779763, 15804901, 23102271, 33685239
Offset: 0

Views

Author

Ilya Gutkovskiy, Mar 04 2019

Keywords

Crossrefs

Cf. A032020, A204858, A206138.

Programs

  • Mathematica
    nmax = 40; CoefficientList[Series[Sum[k! x^(k (k + 1)/2)/Product[(1 - x^j)^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

A306733 Expansion of Sum_{k>=0} x^(k*(k+1)/2) * Product_{j=1..k} (1 + x^j)^j.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 3, 2, 3, 5, 5, 8, 11, 11, 17, 19, 22, 33, 38, 50, 69, 82, 103, 133, 165, 201, 249, 319, 389, 492, 621, 765, 974, 1206, 1500, 1857, 2302, 2843, 3494, 4311, 5275, 6533, 8027, 9840, 12138, 14903, 18340, 22541, 27619, 33811, 41429, 50682, 61809, 75422, 91807
Offset: 0

Views

Author

Ilya Gutkovskiy, Mar 06 2019

Keywords

Crossrefs

Cf. A053261, A206138, A306706.

Programs

  • Mathematica
    nmax = 54; CoefficientList[Series[Sum[x^(k (k + 1)/2) Product[(1 + x^j)^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
Showing 1-5 of 5 results.

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

Content is available under The OEIS End-User License Agreement.