A203774 - OEIS

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

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OFFSET

1,2

COMMENTS

See A203773.

LINKS

Table of n, a(n) for n=1..13.

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

EXAMPLE

Triangle ( f(n)/(f(k)*f(n-k)) )0<=k<=n begins

1 1

1 10 1

1 390 390 1

1 34000 1326000 34000 1

- Peter Bala, Sep 21 2013

MATHEMATICA

(See A203773.)

CROSSREFS

Cf. A203750, A203773.