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.

A377445 E.g.f. satisfies A(x) = 1/(1 + A(x) * log(1 - x))^2.

Original entry on oeis.org

1, 2, 16, 226, 4678, 128728, 4437416, 184176816, 8949477600, 498611374704, 31343763192144, 2194986671431200, 169478318264408832, 14304849733469090976, 1310439414650613267552, 129495512412669053694720, 13731040497246647099309568, 1555129289690056322821075968
Offset: 0

Views

Author

Seiichi Manyama, Oct 28 2024

Keywords

Crossrefs

Cf. A052803, A377446, A377449.
Cf. A367158.

Programs

  • Mathematica
    Table[2*Sum[(3*k+1)!/(2*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, (3*k+1)!/(2*k+2)!*abs(stirling(n, k, 1)));

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A367158.
a(n) = 2 * Sum_{k=0..n} (3*k+1)!/(2*k+2)! * |Stirling1(n,k)|.
a(n) ~ 27 * n^(n-1) / (2^(5/2) * (exp(4/27) - 1)^(n - 1/2) * exp(23*n/27)). - Vaclav Kotesovec, Aug 27 2025

A377446 E.g.f. satisfies A(x) = 1/(1 + A(x) * log(1 - x))^3.

Original entry on oeis.org

1, 3, 33, 642, 18312, 694242, 32960910, 1883757264, 126015816624, 9664169177136, 836144408644560, 80584887639709296, 8562470160920850144, 994509363776066618256, 125361725299037966371824, 17045520282440541500805504, 2486876242354800277464657792, 387527092638347603108279296512
Offset: 0

Views

Author

Seiichi Manyama, Oct 28 2024

Keywords

Crossrefs

Cf. A052803, A377445, A377449.
Cf. A377447.

Programs

  • PARI
    a(n) = 3*sum(k=0, n, (4*k+2)!/(3*k+3)!*abs(stirling(n, k, 1)));

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A377447.
a(n) = 3 * Sum_{k=0..n} (4*k+2)!/(3*k+3)! * |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

Cf. A377448, A377449.
Cf. A377492.

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.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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