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.

A376041 E.g.f. satisfies A(x) = (-log(1 - x / (1 - A(x))^3)) / (1 - A(x)).

Original entry on oeis.org

0, 1, 9, 191, 6496, 305164, 18317390, 1339293822, 115492112640, 11476262240520, 1291250885222592, 162271449317302632, 22528350072978189600, 3424249337820235241472, 565573503590604522245136, 100864333223422171393303488, 19317041144591537348567168256
Offset: 0

Views

Author

Seiichi Manyama, Sep 07 2024

Keywords

Crossrefs

Programs

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

Formula

a(n) = Sum_{k=1..n} (3*n+2*k-2)!/(3*n+k-1)! * |Stirling1(n,k)|.
E.g.f.: Series_Reversion( (1 - x)^3 * (1 - exp(-x * (1 - x))) ).

A376038 E.g.f. satisfies A(x) = (-log(1 - x / (1 - A(x))^3)) * (1 - A(x))^2.

Original entry on oeis.org

0, 1, 3, 29, 466, 10444, 300296, 10539738, 436831368, 20879226240, 1130604893016, 68406042884376, 4573574072262240, 334855813955693952, 26645202689658107712, 2289609993045578793120, 211302073839493597484160, 20844012997702684830894336
Offset: 0

Views

Author

Seiichi Manyama, Sep 07 2024

Keywords

Crossrefs

Programs

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

Formula

a(n) = Sum_{k=1..n} (3*n-k-2)!/(3*n-2*k-1)! * |Stirling1(n,k)|.
E.g.f.: Series_Reversion( (1 - x)^3 * (1 - exp(-x / (1 - x)^2)) ).

A376040 E.g.f. satisfies A(x) = -log(1 - x / (1 - A(x))^3).

Original entry on oeis.org

0, 1, 7, 119, 3258, 123414, 5978082, 352880562, 24573720672, 1972239280488, 179250831525720, 18197871488362752, 2041093578923498448, 250654006995798120480, 33449544716000374458000, 4819960747934844400104480, 745867334512204468875843840
Offset: 0

Views

Author

Seiichi Manyama, Sep 07 2024

Keywords

Crossrefs

Programs

  • PARI
    my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(serreverse((1-x)^3*(1-exp(-x))))))
    
  • PARI
    a(n) = sum(k=1, n, (3*n+k-2)!/(3*n-1)!*abs(stirling(n, k, 1)));

Formula

E.g.f.: Series_Reversion( (1 - x)^3 * (1 - exp(-x)) ).
a(n) = Sum_{k=1..n} (3*n+k-2)!/(3*n-1)! * |Stirling1(n,k)|.
Showing 1-3 of 3 results.