The On-Line Encyclopedia of Integer Sequences (OEIS)

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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.
(history; published version)

#9 by Alois P. Heinz at Wed Feb 08 09:49:10 EST 2023

STATUS

proposed

approved

#8 by Michel Marcus at Wed Feb 08 08:44:23 EST 2023

STATUS

editing

proposed

#7 by Michel Marcus at Wed Feb 08 08:43:44 EST 2023

DATA

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

EXAMPLE

1

1 2

1 6 4

1 24 210 8

1 120 332640 32760 16

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

{ for(row=0, 7, print(A112356(row)); ); } \\ R. J. Mathar, May 19 2006

STATUS

approved

editing

Discussion

Wed Feb 08

08:44

Michel Marcus: one more term to get last row complete

#6 by N. J. A. Sloane at Thu Dec 05 19:57:05 EST 2013

AUTHOR

_Amarnath Murthy (amarnath_murthy(AT)yahoo.com), _, Sep 05 2005

Discussion

Thu Dec 05

19:57

OEIS Server: https://oeis.org/edit/global/2075

#5 by Russ Cox at Fri Mar 30 17:39:07 EDT 2012

PROG

Discussion

Fri Mar 30

17:39

OEIS Server: https://oeis.org/edit/global/190

#4 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

PROG

KEYWORD

easy,nonn,tabl,new

#3 by N. J. A. Sloane at Fri Sep 29 03:00:00 EDT 2006

PROG

KEYWORD

easy,nonn,tabl,new

#2 by N. J. A. Sloane at Fri May 19 03:00:00 EDT 2006

NAME

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 so such that the product of all the terms of the row is (2^n)!. Sequence contains the triangle read by rows.

DATA

KEYWORD

easy,more,nonn,tabl,new

EXTENSIONS

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

#1 by N. J. A. Sloane at Wed Sep 21 03:00:00 EDT 2005

NAME

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 so that the product of all the terms of the row is (2^n)!. Sequence contains the triangle read by rows.

DATA

1, 1, 2, 1, 6, 4, 1, 24, 210, 8, 1, 120, 332640, 32760, 16

OFFSET

0,3

COMMENTS

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

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)

CROSSREFS

Cf. A112357.

KEYWORD

easy,more,nonn,tabl

AUTHOR

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 05 2005

STATUS

approved