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.

A353881 Expansion of e.g.f. 1/(1 + (x * log(1-x))^3 / 36).

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 20, 210, 1960, 18900, 194880, 2166780, 26356880, 349806600, 5029088064, 77748751080, 1284349422720, 22551300670080, 419191223208384, 8222848137607680, 169760091173740800, 3679746265902067200, 83564915096633308800, 1984162781781147770880
Offset: 0

Views

Author

Seiichi Manyama, May 09 2022

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+(x*log(1-x))^3/36)))
    
  • PARI
    a(n) = n!*sum(k=0, n\6, (3*k)!*abs(stirling(n-3*k, 3*k, 1))/(36^k*(n-3*k)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/6)} (3*k)! * |Stirling1(n-3*k,3*k)|/(36^k * (n-3*k)!).

A353883 Expansion of e.g.f. 1/(1 - (x * (exp(x) - 1))^2 / 4).

Original entry on oeis.org

1, 0, 0, 0, 6, 30, 105, 315, 3388, 47628, 497115, 4172025, 37829946, 491971194, 7699457857, 114432747975, 1602464966040, 23767387469688, 408590795439351, 7756561553900085, 149537297087139910, 2889288053301888630, 58297667473293537597
Offset: 0

Views

Author

Seiichi Manyama, May 09 2022

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(x*(exp(x)-1))^2/4)))
    
  • PARI
    a(n) = n!*sum(k=0, n\4, (2*k)!*stirling(n-2*k, 2*k, 2)/(4^k*(n-2*k)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (2*k)! * Stirling2(n-2*k,2*k)/(4^k * (n-2*k)!).

A353885 Expansion of e.g.f. 1/(1 - (x * (exp(x) - 1))^4 / 576).

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 70, 1260, 13650, 115500, 841995, 5555550, 34139105, 198948750, 1175994820, 10315705400, 192609389700, 4563951046200, 98992258506345, 1898260633492650, 32787422848455275, 520556451785466250, 7722233521138092726, 108688302800107222500
Offset: 0

Views

Author

Seiichi Manyama, May 09 2022

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(x*(exp(x)-1))^4/576)))
    
  • PARI
    a(n) = n!*sum(k=0, n\8, (4*k)!*stirling(n-4*k, 4*k, 2)/(576^k*(n-4*k)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/8)} (4*k)! * Stirling2(n-4*k,4*k)/(576^k * (n-4*k)!).

A353895 Expansion of e.g.f. exp( (x * (exp(x) - 1))^3 / 36 ).

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 20, 210, 1400, 7560, 36120, 159390, 850300, 9875580, 170133964, 2688015330, 36706233200, 444802722000, 4939264076016, 52543545234534, 583037908936500, 7645631225897700, 124931080233222340, 2327407301807577066, 44282377224446369800
Offset: 0

Views

Author

Seiichi Manyama, May 09 2022

Keywords

Crossrefs

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x*(exp(x)-1))^3/36)))
    
  • PARI
    a(n) = n!*sum(k=0, n\6, (3*k)!*stirling(n-3*k, 3*k, 2)/(36^k*k!*(n-3*k)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/6)} (3*k)! * Stirling2(n-3*k,3*k)/(36^k * k! * (n-3*k)!).
Showing 1-4 of 4 results.