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.

A273661 Number of forests of labeled rooted trees of height at most 1, with 2n labels, n of which are used for root nodes and any root may contain >= 1 labels.

Original entry on oeis.org

1, 2, 30, 1040, 59850, 5020092, 568136184, 82506827832, 14838761544750, 3218688299529560, 824939949711312292, 245760625104930199992, 83971523217039191918912, 32541316683315808775379000, 14168363320559065768499122200, 6874922021593176730438764171840
Offset: 0

Views

Author

Alois P. Heinz, May 27 2016

Keywords

Crossrefs

Cf. A143396.

Programs

  • Maple
    a:= n-> binomial(2*n,n)*add(Stirling2(n,j)*j^n, j=0..n):
    seq(a(n), n=0..20);
  • Mathematica
    a[0] = 1; a[n_] := Binomial[2*n, n]*Sum[StirlingS2[n, j]*j^n, {j, 0, n}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 27 2017, translated from Maple *)

Formula

a(n) = (2n)!/n! * [x^n] Sum_{j=0..n} Stirling2(n,j)*exp(x)^j.
a(n) = C(2*n,n) * Sum_{j=0..n} Stirling2(2*n,j) * j^n.
a(n) = A143396(2n,n).