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 1-4 of 4 results.

A363639 Expansion of Sum_{k>0} (1/(1 - k*x^k)^3 - 1).

Original entry on oeis.org

3, 12, 19, 51, 36, 180, 57, 405, 352, 918, 111, 3990, 144, 5064, 6534, 15945, 222, 51462, 267, 99354, 82478, 160812, 369, 808490, 66051, 861630, 1090342, 2593614, 552, 8966414, 621, 13039761, 13831470, 22415778, 3166218, 114011229, 852, 110103540, 167426822
Offset: 1

Views

Author

Seiichi Manyama, Jun 13 2023

Keywords

Crossrefs

Cf. A338662, A362683, A363640.
Cf. A363642, A363643, A363644.
Cf. A363628, A363647.

Programs

  • Mathematica
    a[n_] := DivisorSum[n, (n/#)^# * Binomial[# + 2, 2] &]; Array[a, 40] (* Amiram Eldar, Jul 17 2023 *)
  • PARI
    a(n) = sumdiv(n, d, (n/d)^d*binomial(d+2, 2));

Formula

a(n) = Sum_{d|n} (n/d)^d * binomial(d+2,2).

A363642 Expansion of Sum_{k>0} x^k/(1 - k*x^k)^3.

Original entry on oeis.org

1, 4, 7, 17, 16, 55, 29, 129, 100, 311, 67, 1135, 92, 1919, 1486, 5409, 154, 17038, 191, 33491, 20938, 67871, 277, 262861, 9701, 373127, 296110, 978727, 436, 3134821, 497, 5051969, 3898522, 10027655, 474146, 39352069, 704, 49808159, 48362926, 127403221, 862, 411286429, 947
Offset: 1

Views

Author

Seiichi Manyama, Jun 13 2023

Keywords

Crossrefs

Cf. A363639, A363643, A363644.
Cf. A167531, A363645.
Cf. A007437, A363650.

Programs

  • Mathematica
    a[n_] := DivisorSum[n, (n/#)^(#-1) * Binomial[# + 1, 2] &]; Array[a, 50] (* Amiram Eldar, Jul 18 2023 *)
  • PARI
    a(n) = sumdiv(n, d, (n/d)^(d-1)*binomial(d+1, 2));

Formula

a(n) = Sum_{d|n} (n/d)^(d-1) * binomial(d+1,2).

A363643 Expansion of Sum_{k>0} x^(2*k)/(1 - k*x^k)^3.

Original entry on oeis.org

0, 1, 3, 7, 10, 22, 21, 53, 45, 126, 55, 373, 78, 764, 390, 2009, 136, 5995, 171, 12501, 5334, 28392, 253, 92353, 1550, 160070, 79110, 394913, 406, 1167406, 465, 2081649, 1083126, 4457010, 69650, 14534659, 666, 22414016, 13818246, 53200481, 820, 158661826, 903
Offset: 1

Views

Author

Seiichi Manyama, Jun 13 2023

Keywords

Crossrefs

Cf. A363639, A363642, A363644.
Cf. A363651.

Programs

  • Mathematica
    a[n_] := DivisorSum[n, (n/#)^(#-2) * Binomial[#, 2] &]; Array[a, 50] (* Amiram Eldar, Jul 18 2023 *)
  • PARI
    a(n) = sumdiv(n, d, (n/d)^(d-2)*binomial(d, 2));

Formula

a(n) = Sum_{d|n} (n/d)^(d-2) * binomial(d,2).

A363652 Expansion of Sum_{k>0} x^(3*k)/(1 - (k*x)^k)^3.

Original entry on oeis.org

0, 0, 1, 3, 6, 11, 15, 33, 29, 132, 45, 777, 66, 3918, 4466, 22377, 120, 311655, 153, 992586, 7971806, 2949330, 231, 483657349, 58594026, 69206316, 10847774018, 64754136132, 378, 696335917637, 435, 23096840946129, 12709329142142, 32212255248, 1434580813047030
Offset: 1

Views

Author

Seiichi Manyama, Jun 13 2023

Keywords

Crossrefs

Cf. A363647, A363650, A363651.
Cf. A363644.

Programs

  • Mathematica
    a[n_] := DivisorSum[n, (n/#)^(n - 3*n/#)*Binomial[# - 1, 2] &]; Array[a, 35] (* Amiram Eldar, Jul 18 2023 *)
  • PARI
    a(n) = sumdiv(n, d, (n/d)^(n-3*n/d)*binomial(d-1, 2));

Formula

a(n) = Sum_{d|n} (n/d)^(n-3*n/d) * binomial(d-1,2).
Showing 1-4 of 4 results.

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