The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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). 2
 1, 2, 14, 178, 3270, 78316, 2308876, 80775780, 3269037596, 150194207800, 7721544428136, 439128840082648, 27369393580944520, 1855079496872679312, 135846807056384160080, 10688153505317713069936, 899138432350085506208784, 80536073356838110790279200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 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 *) CROSSREFS Main diagonal of A144304. Cf. A001858. Sequence in context: A336635 A352761 A208195 * A285270 A109520 A210097 Adjacent sequences: A252724 A252725 A252726 * A252728 A252729 A252730 KEYWORD nonn AUTHOR Alois P. Heinz, Dec 20 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 8 08:22 EST 2022. Contains 358693 sequences. (Running on oeis4.)