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.

A377449 E.g.f. satisfies A(x) = 1/(1 + A(x) * log(1 - x))^4.

Original entry on oeis.org

1, 4, 56, 1388, 50444, 2436176, 147308248, 10720410984, 913099165080, 89150817350880, 9819313409197632, 1204676163038931744, 162935364815509750368, 24088567621306193343360, 3864931159784777490964608, 668886871993798772730203136, 124209455281616641852564586496
Offset: 0

Views

Author

Seiichi Manyama, Oct 28 2024

Keywords

Crossrefs

Programs

  • PARI
    a(n) = 4*sum(k=0, n, (5*k+3)!/(4*k+4)!*abs(stirling(n, k, 1)));

Formula

E.g.f.: B(x)^4, where B(x) is the e.g.f. of A377448.
a(n) = 4 * Sum_{k=0..n} (5*k+3)!/(4*k+4)! * |Stirling1(n,k)|.

A377447 E.g.f. satisfies A(x) = 1/(1 + A(x)^3 * log(1 - x)).

Original entry on oeis.org

1, 1, 9, 158, 4246, 154924, 7162292, 401410680, 26453842848, 2004890580840, 171808440737928, 16427634731841552, 1733913231506623632, 200249346295125726624, 25118871041680870112352, 3400884689353492497349248, 494317826168209713209318400, 76773315675375252953433141120
Offset: 0

Views

Author

Seiichi Manyama, Oct 28 2024

Keywords

Crossrefs

Programs

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

Formula

a(n) = Sum_{k=0..n} (4*k)!/(3*k+1)! * |Stirling1(n,k)|.

A377411 E.g.f. satisfies A(x) = 1/(1 + A(x)^2 * log(1 - x))^2.

Original entry on oeis.org

1, 2, 24, 550, 19094, 895148, 53013508, 3799302288, 319804780896, 30933514927968, 3381310375415952, 412231069711808400, 55460578942028274960, 8162361371407306334880, 1304519342283397587813600, 224999768419814742497623680, 41656460732290876726281018240
Offset: 0

Views

Author

Seiichi Manyama, Oct 29 2024

Keywords

Crossrefs

Programs

  • Mathematica
    Table[2 * Sum[(5*k+1)!/(4*k+2)! * Abs[StirlingS1[n,k]], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Aug 27 2025 *)
  • PARI
    a(n) = 2*sum(k=0, n, (5*k+1)!/(4*k+2)!*abs(stirling(n, k, 1)));

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377448.
a(n) = 2 * Sum_{k=0..n} (5*k+1)!/(4*k+2)! * |Stirling1(n,k)|.
a(n) ~ 625 * n^(n-1) / (256 * (exp(256/3125) - 1)^(n - 1/2) * exp(2869*n/3125)). - Vaclav Kotesovec, Aug 27 2025
Showing 1-3 of 3 results.