OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..57
FORMULA
a(n) = n! * Sum_{k=0..n} Stirling1(n, k)*binomial(2^k, n). - Vladeta Jovovic, Nov 07 2003
a(n) = Sum_{i=0..n} Sum_{j=0..n} stirling1(n, i) * stirling1(n, j) * 2^(i*j). - Max Alekseyev, Nov 07 2003
a(n) ~ 2^(n^2). - Vaclav Kotesovec, Jul 02 2016
a(n) = A181230(n,n).
EXAMPLE
a(2) = 10: 00/01, 00/10, 01/00, 01/10, 01/11, 10/00, 10/01, 10/11, 11/01, 11/10.
MATHEMATICA
Table[n!*Sum[StirlingS1[n, k]*Binomial[2^k, n], {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Jul 02 2016 *)
PROG
(Magma)
A088310:= func< n | Factorial(n)*(&+[Binomial(2^k, n)*StirlingFirst(n, k): k in [0..n]]) >;
[A088310(n): n in [0..30]]; // G. C. Greubel, Dec 14 2022
(SageMath)
@CachedFunction
def A088310(n): return (-1)^n*factorial(n)*sum((-1)^k*binomial(2^k, n)*stirling_number1(n, k) for k in (0..n))
[A088310(n) for n in range(31)] # G. C. Greubel, Dec 14 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 07 2003
EXTENSIONS
Suggested by Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 06 2003
a(0)-a(5) from W. Edwin Clark, Nov 07 2003
STATUS
approved