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.

A375870 E.g.f. satisfies A(x) = exp( 2 * (exp(x*A(x)^(3/2)) - 1) ).

Original entry on oeis.org

1, 2, 18, 310, 8038, 280264, 12313242, 653591922, 40704551630, 2910862397646, 235114931752898, 21172206066055312, 2103333121459719446, 228525476912967164714, 26957670075375556803178, 3431314158743477432894790, 468762478424957403561956702
Offset: 0

Views

Author

Seiichi Manyama, Sep 01 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = 2*sum(k=0, n, (3*n+2)^(k-1)*stirling(n, k, 2));

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A349683.
a(n) = 2 * Sum_{k=0..n} (3*n+2)^(k-1) * Stirling2(n,k).

A375871 E.g.f. satisfies A(x) = exp( 3 * (exp(x*A(x)) - 1) ).

Original entry on oeis.org

1, 3, 30, 543, 14493, 515001, 22930869, 1229340027, 77151412902, 5551075890453, 450607640485269, 40745592546015495, 4061982705195354033, 442649982865922396337, 52351468801767526253538, 6678605910447082873015923, 914198409310749883430655441
Offset: 0

Views

Author

Seiichi Manyama, Sep 01 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = 3*sum(k=0, n, (3*n+3)^(k-1)*stirling(n, k, 2));

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A349683.
a(n) = 3 * Sum_{k=0..n} (3*n+3)^(k-1) * Stirling2(n,k).

A375872 E.g.f. satisfies A(x) = exp( 4 * (exp(x*A(x)^(3/4)) - 1) ).

Original entry on oeis.org

1, 4, 44, 836, 22980, 832888, 37615340, 2038258804, 128989219860, 9343113460308, 762596057754748, 69273095355130488, 6932765720797549924, 758009268677055714964, 89907747171907593677068, 11498798927333436173636612, 1577528093912610651931113908
Offset: 0

Views

Author

Seiichi Manyama, Sep 01 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = 4*sum(k=0, n, (3*n+4)^(k-1)*stirling(n, k, 2));

Formula

E.g.f.: B(x)^4, where B(x) is the e.g.f. of A349683.
a(n) = 4 * Sum_{k=0..n} (3*n+4)^(k-1) * Stirling2(n,k).

A362467 E.g.f. satisfies log(A(x)) = exp(x / A(x)^2) - 1.

Original entry on oeis.org

1, 1, -2, 11, -97, 1162, -17401, 309297, -6284804, 141430821, -3411964025, 84469913200, -1971020234987, 31982106694501, 703663251081166, -131978337454653865, 11571772746664732291, -879307513026396837470, 64266964230133042267891
Offset: 0

Views

Author

Seiichi Manyama, May 26 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, (-2*n+1)^(k-1)*stirling(n, k, 2));

Formula

a(n) = Sum_{k=0..n} (-2*n+1)^(k-1) * Stirling2(n,k).

A363302 E.g.f. satisfies log(A(x)) = exp(x / A(x)^3) - 1.

Original entry on oeis.org

1, 1, -4, 41, -681, 15667, -460903, 16519141, -698242716, 34004778783, -1874858325725, 115438582354977, -7851013349413919, 584508287058281419, -47281383017104676456, 4129206143361098225405, -387216724567657721607901, 38806186875022459923785751
Offset: 0

Views

Author

Seiichi Manyama, May 26 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=0, n, (-3*n+1)^(k-1)*stirling(n, k, 2));

Formula

a(n) = Sum_{k=0..n} (-3*n+1)^(k-1) * Stirling2(n,k).
Showing 1-5 of 5 results.