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.

A357901 a(n) = Sum_{k=0..floor(n/3)} |Stirling1(n - 2*k,k)|.

Original entry on oeis.org

1, 0, 0, 1, 1, 2, 7, 27, 131, 771, 5320, 42119, 376174, 3740018, 40956593, 489749100, 6348744124, 88677555115, 1327628770657, 21208195526882, 360053293342379, 6473501562355779, 122874692176838047, 2455382300127368557, 51524333987938459606, 1132787775301639812263
Offset: 0

Views

Author

Seiichi Manyama, Oct 19 2022

Keywords

Crossrefs

Cf. A000142, A343579, A357902.

Programs

  • PARI
    a(n) = sum(k=0, n\3, abs(stirling(n-2*k, k, 1)));
  • PARI
    my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, j+x^2)))

Formula

G.f.: Sum_{k>=0} x^k * Product_{j=0..k-1} (j + x^2).

A357920 a(n) = Sum_{k=0..floor(n/5)} Stirling1(n - 4*k,k).

Original entry on oeis.org

1, 0, 0, 0, 0, 1, -1, 2, -6, 24, -119, 717, -5029, 40270, -362606, 3627037, -39903738, 478892051, -6225994449, 87167664184, -1307553837291, 20921303563234, -355667626509575, 6402090252833481, -121640761396741607, 2432831275825738669, -51089718792714854191
Offset: 0

Views

Author

Seiichi Manyama, Oct 20 2022

Keywords

Crossrefs

Cf. A357902, A357919.

Programs

  • PARI
    a(n) = sum(k=0, n\5, stirling(n-4*k, k, 1));
  • PARI
    my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (-x)^k*prod(j=0, k-1, j-x^4)))

Formula

G.f.: Sum_{k>=0} (-x)^k * Product_{j=0..k-1} (j - x^4).

A357932 a(n) = Sum_{k=0..floor(n/4)} |Stirling1(n - 3*k,n - 4*k)|.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 4, 7, 11, 18, 33, 64, 122, 227, 428, 838, 1684, 3396, 6841, 13912, 28787, 60398, 127559, 270687, 579055, 1251706, 2730345, 5994501, 13238058, 29436628, 65951104, 148777927, 337606123, 770418129, 1768566987, 4084504483, 9486890220
Offset: 0

Views

Author

Seiichi Manyama, Oct 21 2022

Keywords

Crossrefs

Cf. A124380, A357931, A357933.
Cf. A353225, A357902, A357926.

Programs

  • PARI
    a(n) = sum(k=0, n\4, abs(stirling(n-3*k, n-4*k, 1)));
  • PARI
    my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, 1+j*x^3)))

Formula

G.f.: Sum_{k>=0} x^k * Product_{j=0..k-1} (1 + j * x^3).

A357922 a(n) = Sum_{k=0..floor(n/5)} |Stirling1(n - 4*k,k)|.

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 1, 2, 6, 24, 121, 723, 5051, 40370, 363154, 3630565, 39929874, 479111219, 6228047601, 87188921464, 1307794924973, 20924276449014, 355707232027825, 6402657184129671, 121649439722758345, 2432972744390660437, 51092165603897459951
Offset: 0

Views

Author

Seiichi Manyama, Oct 20 2022

Keywords

Crossrefs

Cf. A000142, A343579, A357901, A357902.
Cf. A357920.

Programs

  • PARI
    a(n) = sum(k=0, n\5, abs(stirling(n-4*k, k, 1)));
  • PARI
    my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, j+x^4)))

Formula

G.f.: Sum_{k>=0} x^k * Product_{j=0..k-1} (j + x^4).
Showing 1-4 of 4 results.

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