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

0,3

Comments

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

Links

Table of n, a(n) for n=0..27.

Example

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)

Prog

(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

Crossrefs

Cf. A112357.

Sequence in context: A078937 A167560 A132159 * A373341 A135885 A162312

Adjacent sequences: A112353 A112354 A112355 * A112357 A112358 A112359

Keyword

easy,nonn,tabl

Author

Amarnath Murthy, Sep 05 2005

Extensions

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

Status

approved