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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.
5

%I #9 Feb 08 2023 09:49:10

%S 1,1,2,1,6,4,1,24,210,8,1,120,332640,32760,16,1,720,29059430400,

%T 19275223968000,20389320,32,1,5040,223016017416192000,

%U 1250004633476421848894668800000,28844656968251942737920000,48920775120,64

%N 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.

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

%e Triangle begins:

%e 1

%e 1 2

%e 1 6 4

%e 1 24 210 8

%e 1 120 332640 32760 16

%e ...

%e The row for n = 3 is

%e 1 3 3 1

%e 1 (2*3*4) (5*6*7) 8 or (1 24 210 8)

%o (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); }

%o { for(row=0,7, print(A112356(row)); ); } \\ _R. J. Mathar_, May 19 2006

%Y Cf. A112357.

%K easy,nonn,tabl

%O 0,3

%A _Amarnath Murthy_, Sep 05 2005

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