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 1-9 of 9 results.

A371119 E.g.f. satisfies A(x) = 1 + x*A(x)*(exp(x*A(x)) - 1).

Original entry on oeis.org

1, 0, 2, 3, 52, 305, 4866, 57337, 1048776, 18547713, 407900710, 9436057961, 248501026236, 7021087254337, 217488458525898, 7223642070331065, 258233053457437456, 9841074705853124609, 399304906991091898830, 17163110041947804495817, 779646387683354742170820
Offset: 0

Views

Author

Seiichi Manyama, Mar 11 2024

Keywords

Crossrefs

Programs

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

Formula

a(n) = (n!)^2 * Sum_{k=0..floor(n/2)} Stirling2(n-k,k)/( (n-k)! * (n-k+1)! ).
E.g.f.: (1/x) * Series_Reversion( x/(1 + x*(exp(x) - 1)) ). - Seiichi Manyama, Sep 19 2024

A371229 E.g.f. satisfies A(x) = 1 - x*A(x)^2*log(1 - x*A(x)^2).

Original entry on oeis.org

1, 0, 2, 3, 104, 630, 19944, 259560, 8718464, 185086944, 6914815200, 206059083120, 8700740615808, 332779651158240, 15916427365716864, 738672634596405600, 39847940942657495040, 2163098542598925281280, 130682368989193123952640
Offset: 0

Views

Author

Seiichi Manyama, Mar 15 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = n!*(2*n)!*sum(k=0, n\2, abs(stirling(n-k, k, 1))/((n-k)!*(2*n-k+1)!));

Formula

a(n) = n! * (2*n)! * Sum_{k=0..floor(n/2)} |Stirling1(n-k,k)|/( (n-k)! * (2*n-k+1)! ).

A371228 E.g.f. satisfies A(x) = 1 - x*A(x)*log(1 - x*A(x)^2).

Original entry on oeis.org

1, 0, 2, 3, 80, 510, 12084, 164640, 4272736, 91935648, 2769703920, 80692896240, 2849745645504, 103479044628960, 4250475820200960, 183436357950387360, 8649275730513361920, 430735131434242736640, 22999938416454315239424, 1295673669960473064844800
Offset: 0

Views

Author

Seiichi Manyama, Mar 15 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = n!*sum(k=0, n\2, (2*n-k)!*abs(stirling(n-k, k, 1))/((n-k)!*(2*n-2*k+1)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (2*n-k)! * |Stirling1(n-k,k)|/( (n-k)! * (2*n-2*k+1)! ).

A371122 E.g.f. satisfies A(x) = 1 - x*A(x)^3*log(1 - x*A(x)).

Original entry on oeis.org

1, 0, 2, 3, 104, 570, 19284, 220500, 7975008, 148889664, 5911249680, 157016471040, 6913129099392, 239681708117280, 11734594390915200, 501510627153244800, 27265653826293749760, 1380895751066249779200, 83060557136719693406208
Offset: 0

Views

Author

Seiichi Manyama, Mar 11 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = n!*sum(k=0, n\2, (n+2*k)!*abs(stirling(n-k, k, 1))/((n-k)!*(n+k+1)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (n+2*k)! * |Stirling1(n-k,k)|/( (n-k)! * (n+k+1)! ).

A371231 E.g.f. satisfies A(x) = 1 - x*A(x)^3*log(1 - x*A(x)^3).

Original entry on oeis.org

1, 0, 2, 3, 152, 930, 42804, 574140, 27267456, 613793376, 31378237200, 1021391030880, 57256014687552, 2456525677525920, 152135168050833408, 8093376365276966400, 554533365688970342400, 35081649646969248529920, 2653840371674014197608448
Offset: 0

Views

Author

Seiichi Manyama, Mar 15 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = n!*(3*n)!*sum(k=0, n\2, abs(stirling(n-k, k, 1))/((n-k)!*(3*n-k+1)!));

Formula

a(n) = n! * (3*n)! * Sum_{k=0..floor(n/2)} |Stirling1(n-k,k)|/( (n-k)! * (3*n-k+1)! ).

A371138 E.g.f. satisfies A(x) = 1 - x^2*A(x)^2*log(1 - x*A(x)).

Original entry on oeis.org

1, 0, 0, 6, 12, 40, 2340, 18648, 154560, 5767200, 95911200, 1438778880, 48014778240, 1228487644800, 27997623029376, 972327510000000, 32550437645107200, 1006902423902269440, 38894136241736494080, 1569697954634035537920, 61093442927846310912000
Offset: 0

Views

Author

Seiichi Manyama, Mar 12 2024

Keywords

Crossrefs

Programs

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

Formula

a(n) = (n!)^2 * Sum_{k=0..floor(n/3)} |Stirling1(n-2*k,k)|/( (n-2*k)! * (n-k+1)! ).
E.g.f.: (1/x) * Series_Reversion( x/(1 - x^2*log(1 - x)) ). - Seiichi Manyama, Sep 19 2024

A377390 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - x*log(1-x))^2 ).

Original entry on oeis.org

1, 0, 4, 6, 232, 1380, 46308, 593880, 20639456, 434113344, 16557009840, 490894572960, 20995513516800, 801146038080960, 38632110899469696, 1791609186067646400, 97167945389675212800, 5275541489312858803200, 319879838094553691744256, 19820894989178283188198400
Offset: 0

Views

Author

Seiichi Manyama, Oct 27 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = 2*n!*(2*n+1)!*sum(k=0, n\2, abs(stirling(n-k, k, 1))/((n-k)!*(2*n-k+2)!));

Formula

E.g.f. A(x) satisfies A(x) = ( 1 - x*A(x)*log(1 - x*A(x)) )^2.
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A371229.
a(n) = 2 * n! * (2*n+1)! * Sum_{k=0..floor(n/2)} |Stirling1(n-k,k)|/( (n-k)! * (2*n-k+2)! ).

A377391 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - x*log(1-x))^3 ).

Original entry on oeis.org

1, 0, 6, 9, 528, 3150, 157032, 2060100, 102770112, 2276373456, 120136435200, 3868551141840, 221493499198848, 9438561453784320, 592954244405195904, 31417910131585330080, 2173884244961012121600, 137231093173511486016000, 10452538023125775799541760
Offset: 0

Views

Author

Seiichi Manyama, Oct 27 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = 3*n!*(3*n+2)!*sum(k=0, n\2, abs(stirling(n-k, k, 1))/((n-k)!*(3*n-k+3)!));

Formula

E.g.f. A(x) satisfies A(x) = ( 1 - x*A(x)*log(1 - x*A(x)) )^3.
E.g.f.: B(x)^3, where B(x) is the e.g.f. of A371231.
a(n) = 3 * n! * (3*n+2)! * Sum_{k=0..floor(n/2)} |Stirling1(n-k,k)|/( (n-k)! * (3*n-k+3)! ).

A376292 E.g.f. satisfies A(x) = 1 - (x*A(x))^3 * log(1 - x*A(x)).

Original entry on oeis.org

1, 0, 0, 0, 24, 60, 240, 1260, 169344, 1693440, 17150400, 187941600, 12778698240, 271809457920, 5031211086720, 91848556800000, 4643532967772160, 154079136039628800, 4367731446302515200, 117143657916761548800, 5457792037686441984000
Offset: 0

Views

Author

Seiichi Manyama, Sep 19 2024

Keywords

Crossrefs

Programs

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

Formula

a(n) = (n!)^2 * Sum_{k=0..floor(n/4)} |Stirling1(n-3*k,k)|/( (n-3*k)! * (n-k+1)! ).
E.g.f.: (1/x) * Series_Reversion( x/(1 - x^3*log(1 - x)) ).
Showing 1-9 of 9 results.