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.
1, 2, 30, 1040, 59850, 5020092, 568136184, 82506827832, 14838761544750, 3218688299529560, 824939949711312292, 245760625104930199992, 83971523217039191918912, 32541316683315808775379000, 14168363320559065768499122200, 6874922021593176730438764171840
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..252
Crossrefs
Cf. A143396.
Programs
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Maple
a:= n-> binomial(2*n,n)*add(Stirling2(n,j)*j^n, j=0..n): seq(a(n), n=0..20);
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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).