OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
FORMULA
a(n) = Sum_{k=1..n} (k-1)! * A147315(n,k).
a(n) ~ (n-1)! / (arctan(3/4))^n. - Vaclav Kotesovec, Aug 22 2014
MAPLE
T:= proc(n, k) option remember;
if k=n then 1
elif k<0 or k>n then 0
else T(n-1, k-1) +k*T(n-1, k) +k*(k+1)/2 *T(n-1, k+1)
fi
end:
a:= n-> add((k-1)! * T(n, k), k=1..n):
seq(a(n), n=0..20); # Alois P. Heinz, Feb 17 2011
MATHEMATICA
T[n_, k_] := T[n, k] = If[k==n, 1, If[k<0 || k>n, 0, T[n-1, k-1] + k*T[n-1, k] + k*(k+1)/2*T[n-1, k+1]]]; a[n_] := Sum[(k-1)!*T[n, k], {k, 1, n}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Apr 03 2015, after Alois P. Heinz *)
PROG
(Maxima) a[0]:0$a[1]:1$
a[n]:=sum((-1)^floor(p/2)*(mod(p+1, 2)-(-1)^p*4^floor(p/2))*binomial(n-1, p)*a[n-p], p, 1, n-1)-mod(n-1, 2)*(%i)^n;
makelist(a[n], n, 0, 100); /* Tani Akinari, Oct 30 2017 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Feb 17 2011
STATUS
approved