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 1-2 of 2 results.

A385548 E.g.f. A(x) satisfies A(x) = 1 + Sum_{k>=1} k * x^k/k! * A(k*x).

Original entry on oeis.org

1, 1, 4, 27, 340, 7185, 254046, 14579341, 1345796824, 196990674705, 45358607173690, 16288829003062341, 9064769868554283060, 7771093242706161635449, 10211642577081863563621990, 20477419392449457003138477885, 62420691099194078521450782932656
Offset: 0

Views

Author

Seiichi Manyama, Jul 03 2025

Keywords

Crossrefs

Cf. A385544.

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (i-j)^(j+1)*binomial(i, j)*v[j+1])); v;

Formula

a(0) = 1; a(n) = Sum_{k=0..n-1} (n-k)^(k+1) * binomial(n,k) * a(k).

A385585 G.f. A(x) satisfies A(x) = Sum_{k>=0} (k*x)^k * A(k*x).

Original entry on oeis.org

1, 1, 5, 40, 457, 7101, 148270, 4206121, 165267951, 9117777074, 709325010385, 77906424970811, 12109278363587036, 2670187179684919761, 836451775445907622685, 372646977140600929476104, 236390047765997660237447061, 213719117789650238860723125601
Offset: 0

Views

Author

Seiichi Manyama, Jul 03 2025

Keywords

Crossrefs

Programs

  • Mathematica
    a[0] = 1; a[n_] := a[n] = Sum[(n-k)^n * a[k], {k, 0, n-1}]; Table[a[n], {n, 0, 20}] (* Vaclav Kotesovec, Jul 04 2025 *)
  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (i-j)^i*v[j+1])); v;

Formula

a(0) = 1; a(n) = Sum_{k=0..n-1} (n-k)^n * a(k).
From Vaclav Kotesovec, Jul 04 2025: (Start)
a(n) ~ c * 3^(n*(n+3)/6), where
c = 14331.87392277329... if mod(n,3) = 0,
c = 14331.87383811849... if mod(n,3) = 1,
c = 14331.87405112061... if mod(n,3) = 2. (End)
Showing 1-2 of 2 results.