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.

A377361 E.g.f. satisfies A(x) = ( 1 - log(1 - x*A(x)) )^3.

Original entry on oeis.org

1, 3, 27, 435, 10308, 324942, 12831540, 610024398, 33948639024, 2165995595208, 155913776865216, 12501945620113320, 1105228405532295216, 106806396107364409440, 11201958792185117156640, 1267313834232739887340464, 153842580381390055963315200, 19946923686925035463312117632
Offset: 0

Views

Author

Seiichi Manyama, Oct 26 2024

Keywords

Crossrefs

Programs

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A367152.
a(n) = 3 * (3*n+2)! * Sum_{k=0..n} |Stirling1(n,k)|/(3*n-k+3)!.
E.g.f.: (1/x) * Series_Reversion( x/(1 - log(1-x))^3 ).

A377429 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + log(1-x))^4 ).

Original entry on oeis.org

1, 4, 56, 1436, 54540, 2763696, 175688744, 13457185080, 1207241712536, 124205544781728, 14420516981211360, 1865347268407271040, 266056506383725529568, 41485848013549310521536, 7021170794004780911946048, 1281852242007649764308226240, 251124461130948243588667169280
Offset: 0

Views

Author

Seiichi Manyama, Oct 28 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+log(1-x))^4)/x))
    
  • PARI
    a(n) = 4*sum(k=0, n, (4*n+k+3)!*abs(stirling(n, k, 1)))/(4*n+4)!;

Formula

E.g.f. A(x) satisfies A(x) = 1/(1 + log(1 - x*A(x)))^4.
E.g.f.: B(x)^4, where B(x) is the e.g.f. of A377426.
a(n) = (4/(4*n+4)!) * Sum_{k=0..n} (4*n+k+3)! * |Stirling1(n,k)|.

A376394 Expansion of e.g.f. ( (1/x) * Series_Reversion( x*(1 + log(1-x))^3 ) )^(2/3).

Original entry on oeis.org

1, 2, 20, 388, 11382, 449868, 22427988, 1351746912, 95626268208, 7769995319280, 713229439560816, 73000860715645344, 8243857485642410400, 1018250616169754862048, 136561871538665054975520, 19763248903874313555142656, 3069876028020976768409255808, 509447295061343606934940250880
Offset: 0

Views

Author

Seiichi Manyama, Sep 22 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x*(1+log(1-x))^3)/x)^(2/3)))
    
  • PARI
    a(n) = 2*sum(k=0, n, (3*n+k+1)!*abs(stirling(n, k, 1)))/(3*n+2)!;

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A367139.
a(n) = (2/(3*n+2)!) * Sum_{k=0..n} (3*n+k+1)! * |Stirling1(n,k)|.

A376437 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x^2*log(1-x))^3 ).

Original entry on oeis.org

1, 0, 0, 18, 36, 120, 24300, 192024, 1572480, 194205600, 3380922720, 50671716480, 4879442177280, 144175221440640, 3391736273557632, 287077095515548800, 12328722259931750400, 413067654425986560000, 33216197499043235527680
Offset: 0

Views

Author

Seiichi Manyama, Sep 22 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x^2*log(1-x))^3)/x))
    
  • PARI
    a(n) = 3*n!*sum(k=0, n\3, (3*n+k+2)!*abs(stirling(n-2*k, k, 1))/(n-2*k)!)/(3*n+3)!;

Formula

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