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.

A375556 Expansion of e.g.f. 1 / (1 + x * log(1 - x^3/6)).

Original entry on oeis.org

1, 0, 0, 0, 4, 0, 0, 70, 1120, 0, 5600, 184800, 2217600, 1201200, 61661600, 1513512000, 16682265600, 38118080000, 1440863424000, 31721866176000, 352561745536000, 2053230379200000, 68832104140800000, 1449890913639168000, 17583390443114496000
Offset: 0

Views

Author

Seiichi Manyama, Aug 19 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x^3/6))))
    
  • PARI
    a(n) = n!*sum(k=0, n\3, (n-3*k)!*abs(stirling(k, n-3*k, 1))/(6^k*k!));

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k)! * |Stirling1(k,n-3*k)|/(6^k*k!).

A375237 Expansion of e.g.f. 1 / (1 + x * log(1 - x^2/2))^2.

Original entry on oeis.org

1, 0, 0, 6, 0, 30, 540, 420, 15120, 192780, 623700, 15467760, 187110000, 1394593200, 30353483160, 401350950000, 4974611241600, 105201040744800, 1624218256861200, 27525899782180800, 599214125325816000, 10967831645346576000, 227431647445400798400
Offset: 0

Views

Author

Seiichi Manyama, Aug 23 2024

Keywords

Crossrefs

Programs

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A375167.
a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k+1)! * |Stirling1(k,n-2*k)|/(2^k*k!).

A375558 Expansion of e.g.f. 1 / (1 + x * log(1 - x^4/24)).

Original entry on oeis.org

1, 0, 0, 0, 0, 5, 0, 0, 0, 315, 6300, 0, 0, 150150, 6306300, 94594500, 0, 268017750, 17689171500, 549972423000, 7332965640000, 1283268987000, 117632990475000, 5681673439942500, 155840185781280000, 1961530116170625000, 1606200062942475000
Offset: 0

Views

Author

Seiichi Manyama, Aug 19 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x^4/24))))
    
  • PARI
    a(n) = n!*sum(k=0, n\4, (n-4*k)!*abs(stirling(k, n-4*k, 1))/(24^k*k!));

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (n-4*k)! * |Stirling1(k,n-4*k)|/(24^k*k!).

A375586 Expansion of e.g.f. 1 / (1 + x - x * exp(x^2/2)).

Original entry on oeis.org

1, 0, 0, 3, 0, 15, 180, 105, 5040, 46305, 132300, 3752595, 33679800, 243378135, 5565940380, 56191160025, 712410098400, 14889814164225, 183558878603100, 3236148386145675, 66650136566013000, 1027807726886515575, 21983938825036488300, 469896981350215644225
Offset: 0

Views

Author

Seiichi Manyama, Aug 19 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-x*exp(x^2/2))))
    
  • PARI
    a(n) = n!*sum(k=0, n\2, (n-2*k)!*stirling(k, n-2*k, 2)/(2^k*k!));

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)! * Stirling2(k,n-2*k)/(2^k*k!).

A375682 Expansion of e.g.f. 1 / (1 + x * log(1 - x^2/2))^3.

Original entry on oeis.org

1, 0, 0, 9, 0, 45, 1080, 630, 30240, 470610, 1247400, 38170440, 523908000, 3454050600, 87950182320, 1245647403000, 14580569203200, 346019491818000, 5524280291930400, 92520760776444000, 2188180621979352000, 40781057935225608000, 857154570994798876800
Offset: 0

Views

Author

Seiichi Manyama, Aug 23 2024

Keywords

Crossrefs

Programs

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A375167.
a(n) = (n!/2) * Sum_{k=0..floor(n/2)} (n-2*k+2)! * |Stirling1(k,n-2*k)|/(2^k*k!).
Showing 1-5 of 5 results.