A093303 a(n) = a(n-1)*(2n-1) + 2n with a(0)=0.

0, 2, 10, 56, 400, 3610, 39722, 516400, 7746016, 131682290, 2501963530, 52541234152, 1208448385520, 30211209638026, 815702660226730, 23655377146575200, 733316691543831232, 24199450820946430690, 846980778733125074186

Offset: 0

Author

Emrehan Halici (emrehan(AT)halici.com.tr), Apr 24 2004

Keywords

• easy
• nonn

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

Crossrefs

Cf. A005843.

Programs

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 *)

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

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

Extensions

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 24 2004