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.

A367489 Expansion of e.g.f. -x * log(3 - 2*exp(x)).

Original entry on oeis.org

0, 0, 4, 18, 120, 1110, 13140, 189042, 3197040, 62093358, 1361253900, 33236925546, 894243758760, 26281928034726, 837663638344260, 28775491618091490, 1059805146165293280, 41657455054069680414, 1740535210734651716220, 77029901631623181859674
Offset: 0

Views

Author

Seiichi Manyama, Nov 19 2023

Keywords

Crossrefs

Programs

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

Formula

a(n) = n * Sum_{k=1..n-1} 2^k * (k-1)! * Stirling2(n-1,k).

A367487 Expansion of e.g.f. 1/(4 - 3*exp(x))^(x/2).

Original entry on oeis.org

1, 0, 3, 18, 195, 2730, 47745, 1001742, 24523401, 686190258, 21601161015, 755533274826, 29066119327179, 1219715093642838, 55441103383640793, 2713468284508412430, 142269924567096468177, 7955396173559375208426, 472576083221524737100311
Offset: 0

Views

Author

Seiichi Manyama, Nov 19 2023

Keywords

Crossrefs

Programs

  • Mathematica
    With[{nn=20},CoefficientList[Series[1/(4-3Exp[x])^(x/2),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 23 2025 *)
  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j*sum(k=1, j-1, 3^k*(k-1)!*stirling(j-1, k, 2))*binomial(i-1, j-1)*v[i-j+1])/2); v;

Formula

a(0) = 1; a(n) = (1/2) * Sum_{k=1..n} A367490(k) * binomial(n-1,k-1) * a(n-k).

A367488 Expansion of e.g.f. 1/(4 - 3*exp(x))^x.

Original entry on oeis.org

1, 0, 6, 36, 444, 6540, 119520, 2593164, 65233392, 1867289868, 59939612040, 2132540249532, 83293357351248, 3543242182036284, 163062595422642552, 8071964230348189260, 427682380939864204224, 24149065480351703398572, 1447640087400503974386504
Offset: 0

Views

Author

Seiichi Manyama, Nov 19 2023

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j*sum(k=1, j-1, 3^k*(k-1)!*stirling(j-1, k, 2))*binomial(i-1, j-1)*v[i-j+1])); v;

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A367490(k) * binomial(n-1,k-1) * a(n-k).
Showing 1-3 of 3 results.