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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.

%I A112356 #9 Feb 08 2023 09:49:10
%S A112356 1,1,2,1,6,4,1,24,210,8,1,120,332640,32760,16,1,720,29059430400,
%T A112356 19275223968000,20389320,32,1,5040,223016017416192000,
%U A112356 1250004633476421848894668800000,28844656968251942737920000,48920775120,64
%N 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.
%C A112356 The leading diagonal contains 2^n. The second column terms are (n+1)!.
%e A112356 Triangle begins:
%e A112356   1
%e A112356   1 2
%e A112356   1 6 4
%e A112356   1 24 210 8
%e A112356   1 120 332640 32760 16
%e A112356 ...
%e A112356 The row for n = 3 is
%e A112356   1 3 3 1
%e A112356   1 (2*3*4) (5*6*7) 8 or (1 24 210 8)
%o A112356 (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 A112356 { for(row=0,7, print(A112356(row)); ); } \\ _R. J. Mathar_, May 19 2006
%Y A112356 Cf. A112357.
%K A112356 easy,nonn,tabl
%O A112356 0,3
%A A112356 _Amarnath Murthy_, Sep 05 2005
%E A112356 More terms from Mandy Stoner (astoner(AT)ashland.edu), Apr 27 2006