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.

Previous Showing 11-14 of 14 results.

A320739 Number of partitions of n with eight sorts of part 1 which are introduced in ascending order.

Original entry on oeis.org

1, 1, 3, 7, 20, 63, 233, 966, 4454, 22403, 121570, 705150, 4337883, 28091897, 190105229, 1334705996, 9656244012, 71551215515, 540187472767, 4137336876098, 32036946594336, 250131019258467, 1965050543015106, 15509209887539395, 122829846706462146
Offset: 0

Views

Author

Alois P. Heinz, Oct 20 2018

Keywords

Links

Crossrefs

Column k=8 of A292745.

Programs

  • Maple
    b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
      Stirling2(n, j), j=0..8), add(b(n-i*j, i-1), j=0..n/i))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..40);
  • Mathematica
    b[n_, i_] := b[n, i] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, 8}], Sum[b[n - i j, i - 1], {j, 0, n/i}]];
a[n_] := b[n, n];
a /@ Range[0, 40] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)

A320740 Number of partitions of n with nine sorts of part 1 which are introduced in ascending order.

Original entry on oeis.org

1, 1, 3, 7, 20, 63, 233, 966, 4454, 22404, 121615, 706306, 4360204, 28452601, 195263881, 1402218667, 10482569938, 81153069799, 647261864569, 5292447172261, 44165731426846, 374675276723042, 3220404743013997, 27967105952549269, 244844437773618386
Offset: 0

Views

Author

Alois P. Heinz, Oct 20 2018

Keywords

Links

Crossrefs

Column k=9 of A292745.

Programs

  • Maple
    b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
      Stirling2(n, j), j=0..9), add(b(n-i*j, i-1), j=0..n/i))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..40);
  • Mathematica
    b[n_, i_] := b[n, i] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, 9}], Sum[b[n - i j, i - 1], {j, 0, n/i}]];
a[n_] := b[n, n];
a /@ Range[0, 40] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)

A320733 Number of partitions of n with two sorts of part 1 which are introduced in ascending order.

Original entry on oeis.org

1, 1, 3, 6, 13, 26, 54, 108, 219, 439, 882, 1766, 3539, 7081, 14172, 28351, 56716, 113443, 226908, 453833, 907698, 1815424, 3630893, 7261829, 14523725, 29047513, 58095121, 116190338, 232380810, 464761759, 929523710, 1859047619, 3718095507, 7436191301
Offset: 0

Views

Author

Alois P. Heinz, Oct 20 2018

Keywords

Links

Crossrefs

Column k=2 of A292745.
Cf. A002865, A011782, A090764.

Programs

  • Maple
    b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
      Stirling2(n, j), j=0..2), add(b(n-i*j, i-1), j=0..n/i))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..40);
  • Mathematica
    b[n_, i_] := b[n, i] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, 2}], Sum[b[n - i j, i - 1], {j, 0, n/i}]];
a[n_] := b[n, n];
a /@ Range[0, 40] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)

Formula

G.f.: ((1 - x)/(1 - 2*x)) * Product_{k>=2} 1/(1 - x^k). - Ilya Gutkovskiy, Dec 03 2019

A320741 Number of partitions of n with ten sorts of part 1 which are introduced in ascending order.

Original entry on oeis.org

1, 1, 3, 7, 20, 63, 233, 966, 4454, 22404, 121616, 706361, 4361910, 28491982, 196018395, 1414922459, 10677120529, 83924901635, 684582037213, 5772723290503, 50123602905429, 446382776341382, 4062023996661972, 37638652689027910, 354017801203414670
Offset: 0

Views

Author

Alois P. Heinz, Oct 20 2018

Keywords

Links

Crossrefs

Column k=10 of A292745.

Programs

  • Maple
    b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
      Stirling2(n, j), j=0..10), add(b(n-i*j, i-1), j=0..n/i))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..40);
  • Mathematica
    b[n_, i_] := b[n, i] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, 10}], Sum[b[n - i j, i - 1], {j, 0, n/i}]];
a[n_] := b[n, n];
a /@ Range[0, 40] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)
Previous Showing 11-14 of 14 results.

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