A203774 Square root of v(2n)/v(2n-1), where v=A203773.

1, 10, 390, 34000, 5255380, 1267531200, 439881715000, 207679463680000, 128024359806330000, 99861207456574720000, 96148662977402249500000, 112000625784958629888000000, 155250403381700932802965000000

Offset: 1

Author

Clark Kimberling, Jan 05 2012

Keywords

• nonn

Comments

See A203773.

Examples

			Triangle ( f(n)/(f(k)*f(n-k)) )0<=k<=n begins
1
1     1
1    10        1
1   390      390      1
1 34000  1326000  34000     1
- _Peter Bala_, Sep 21 2013
		

Crossrefs

Cf. A203750, A203773.

Programs

Mathematica

(See A203773.)

Formula

Define a sequence f(n) by means of the double product f(n) = |product {1 <= a, b <= n} (a + b*i)|, a sort of 2-dimensional analog of n!. Then a(n) = f(n)/(f(1)*f(n-1)) is the first column of the triangle ( f(n)/(f(k)*f(n-k)) ) 0<=k<=n, an analog of Pascal's triangle. - Peter Bala, Sep 21 2013

a(n) = gamma((1-i)*n)*gamma((1+i)*n)*sinh(n*Pi)/Pi (conjecture). - Velin Yanev, Nov 15 2016