OFFSET
0,2
COMMENTS
Obviously, a(n) is always an even number. a(2) and a(6) are even semiprimes. - Altug Alkan, Dec 07 2015
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
a(n) = n!*C(2*n-1,n)/2^(n-1) * Sum_{k=1..n} 2^k*k/(k!*C(2*k-1,k)), for n>0. - Vaclav Kotesovec, Oct 28 2012
From Altug Alkan, Dec 07 2015: (Start)
a(A047212(k)) mod 10 = 0.
a(A016861(k)) mod 10 = 2.
a(A016885(k)) mod 10 = 6. (End)
a(n) ~ (sqrt(2) + 2*sqrt(Pi)*exp(1/2)*erf(1/sqrt(2))) * 2^n * n^n / exp(n). - Vaclav Kotesovec, Dec 18 2015
MATHEMATICA
Flatten[{0, Table[n!*Binomial[2*n-1, n]/2^(n-1)*Sum[2^k*k/(k!*Binomial[2*k-1, k]), {k, 1, n}], {n, 1, 20}]}] (* Vaclav Kotesovec, Oct 28 2012 *)
PROG
(PARI) a(n) = if(n==0, 0, n!*binomial(2*n-1, n)/2^(n-1) * sum(k=1, n, 2^k*k/(k!*binomial(2*k-1, k)))) \\ Altug Alkan, Dec 07 2015
(PARI) a(n) = if(n==0, 0, a(n-1)*(2*n-1) + 2*n); \\ Altug Alkan, Dec 07 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Emrehan Halici (emrehan(AT)halici.com.tr), Apr 24 2004
EXTENSIONS
More terms from Pab Ter (pabrlos(AT)yahoo.com), May 24 2004
STATUS
approved