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.

A377494 E.g.f. satisfies A(x) = 1/(1 + A(x)^2 * log(1 - x*A(x)^2)).

Original entry on oeis.org

1, 1, 11, 248, 8632, 408794, 24550512, 1788220664, 153204336480, 15097630639464, 1682516996213376, 209233809698022240, 28725012833286981456, 4315256340778010888688, 704140465438516958644512, 124020015235118786512297728, 23450965881108082875087150336, 4738390708952218941582313234176
Offset: 0

Views

Author

Seiichi Manyama, Oct 29 2024

Keywords

Crossrefs

Programs

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

Formula

a(n) = Sum_{k=0..n} (2*n+3*k)!/(2*n+2*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

A377493 E.g.f. satisfies A(x) = 1/(1 + A(x) * log(1 - x*A(x)))^3.

Original entry on oeis.org

1, 3, 51, 1695, 85524, 5826402, 501281256, 52178851302, 6378309961152, 895845418408992, 142179729906910680, 25166131508370202776, 4915451890368514588032, 1050225776987234559170976, 243664809398578134394019712, 61008419406811276254021582384
Offset: 0

Views

Author

Seiichi Manyama, Oct 29 2024

Keywords

Crossrefs

Programs

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A377497.
a(n) = 3 * Sum_{k=0..n} (3*n+4*k+2)!/(3*n+3*k+3)! * |Stirling1(n,k)|.
Showing 1-3 of 3 results.