A112356 Following triangle is based on Pascal's triangle. The r-th term of the n-th row is product of C(n,r) successive integers such that the product of all the terms of the row is (2^n)!. Sequence contains the triangle read by rows.

1, 1, 2, 1, 6, 4, 1, 24, 210, 8, 1, 120, 332640, 32760, 16, 1, 720, 29059430400, 19275223968000, 20389320, 32, 1, 5040, 223016017416192000, 1250004633476421848894668800000, 28844656968251942737920000, 48920775120, 64

Offset: 0

Author

Amarnath Murthy, Sep 05 2005

Keywords

• easy
• nonn
• tabl

Comments

The leading diagonal contains 2^n. The second column terms are (n+1)!.

Examples

			Triangle begins:
  1
  1 2
  1 6 4
  1 24 210 8
  1 120 332640 32760 16
...
The row for n = 3 is
  1 3 3 1
  1 (2*3*4) (5*6*7) 8 or (1 24 210 8)
		

Crossrefs

Cf. A112357.

Programs

PARI

A112356(n)= { local(resul,piv,a); resul=[1]; piv=2; for(col=1,n, a=piv; piv++; for(c=2,binomial(n,col), a *= piv; piv++; ); resul=concat(resul,a); ); return(resul); }
{ for(row=0,7, print(A112356(row)); ); } \\ R. J. Mathar, May 19 2006

Extensions

More terms from Mandy Stoner (astoner(AT)ashland.edu), Apr 27 2006