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 1-3 of 3 results.

A353891 Expansion of e.g.f. exp( (x * log(1-x))^2 / 4 ).

Original entry on oeis.org

1, 0, 0, 0, 6, 30, 165, 1050, 8932, 86184, 909360, 10393020, 129313206, 1743627600, 25314159780, 393346535400, 6512022804960, 114430467296880, 2127154061337480, 41703621476302800, 859966710771029040, 18606040434320713920, 421427283751799685360
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*log(1-x))^2/4)))
    
  • PARI
    a(n) = n!*sum(k=0, n\4, (2*k)!*abs(stirling(n-2*k, 2*k, 1))/(4^k*k!*(n-2*k)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (2*k)! * |Stirling1(n-2*k,2*k)|/(4^k * k! * (n-2*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)!).

A353896 Expansion of e.g.f. exp( (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, 1144463320, 8171563400, 112204064700, 2364061354200, 49912312090845, 951208121086650, 16403948060775275, 260328078068154250, 3860274855288458376, 54182965918066177500
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))^4/576)))
    
  • PARI
    a(n) = n!*sum(k=0, n\8, (4*k)!*stirling(n-4*k, 4*k, 2)/(576^k*k!*(n-4*k)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/8)} (4*k)! * Stirling2(n-4*k,4*k)/(576^k * k! * (n-4*k)!).
Showing 1-3 of 3 results.