A252727 a(n) = n-th number of the n-th iteration of the hyperbinomial transform on sequence A001858 (number of forests of trees on n labeled nodes).
1, 2, 14, 178, 3270, 78316, 2308876, 80775780, 3269037596, 150194207800, 7721544428136, 439128840082648, 27369393580944520, 1855079496872679312, 135846807056384160080, 10688153505317713069936, 899138432350085506208784, 80536073356838110790279200
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..200
Programs
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Maple
hymtr:= proc(p) proc(n, m) `if`(m=0, p(n), m* add(p(k)*binomial(n, k) *(n-k+m)^(n-k-1), k=0..n)) end end: f:= proc(n) option remember; add(add(binomial(n-1, n-m-j)* binomial(m, j)*n^(n-m-j)*(m+j)!/(-2)^j/m!, j=0..m), m=0..n) end: A:= hymtr(f): a:= n-> A(n$2): seq(a(n), n=0..20); -
Mathematica
hymtr[p_] := Function[{n, m}, If[m==0, p[n], m*Sum[p[k]*Binomial[n, k]*(n - k + m)^(n-k-1), {k, 0, n}]]]; f[0] = 1; f[n_] := f[n] = Sum[ Sum[ Binomial[m, j] * Binomial[n-1, n-m-j]*n^(n-m-j)*(m+j)!/(-2)^j/m!, {j, 0, m}], {m, 0, n}]; A[0, ] = 1; A[1, k] := k+1; A[n_, m_] := hymtr[f][n, n]; a[n_] := A[n, n]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 26 2017, after Alois P. Heinz *)