OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..183 (terms n=1..19 from R. H. Hardin)
Morton Abramson and David Promislow, Enumeration of arrays by column rises, J. Combinatorial Theory Ser. A 24(2) (1978), 247-250.
FORMULA
a(n) = f(n) * n!, where f(0) = 1, f(n) = Sum_{k=0..n-1} (-1)^(n+k+1) * f(k) * binomial(n, k)^2 / (n-k)!. - Daniel Suteu, Feb 23 2018
a(n) = (n!)^3 * [x^n] 1 / (1 + Sum_{k>=1} (-x)^k / (k!)^3). - Seiichi Manyama, Jul 18 2020
a(n) ~ c * n!^3 / r^n, where r = 1.16151549806386358435938834554462085598002... is the root of the equation HypergeometricPFQ[{}, {1, 1}, -r] = 0 and c = 1.182760720067731330743886867947078139186402925891650811631774628... - Vaclav Kotesovec, Sep 16 2020
EXAMPLE
Some solutions for n=3:
2 1 0 2 0 1 1 2 0 0 2 1 2 0 1 2 1 0 2 1 0
0 2 1 2 0 1 0 2 1 2 1 0 2 1 0 2 1 0 2 0 1
0 2 1 2 1 0 2 0 1 2 0 1 0 1 2 1 2 0 2 0 1
MAPLE
A212856 := proc(n) sum(z^k/k!^3, k = 0..infinity);
series(%^x, z=0, n+1): n!^3*coeff(%, z, n); add(abs(coeff(%, x, k)), k=0..n) end:
seq(A212856(n), n=0..14); # Peter Luschny, May 27 2017
# second Maple program:
a:= proc(n) option remember; `if`(n=0, 1, -add(
binomial(n, j)^3*(-1)^j*a(n-j), j=1..n))
end:
seq(a(n), n=0..15); # Alois P. Heinz, Apr 26 2020
MATHEMATICA
f[0] = 1; f[n_] := f[n] = Sum[(-1)^(n+k+1)*f[k]*Binomial[n, k]^2/(n-k)!, {k, 0, n-1}]; a[n_] := f[n]*n!; Array[a, 14] (* Jean-François Alcover, Feb 27 2018, after Daniel Suteu *)
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 28 2012
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Apr 26 2020
STATUS
approved