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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 20 2014
STATUS
approved