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Search: id:A112356
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| A112356 |
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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. |
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+0
5
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| 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
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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The leading diagonal contains 2^n. The second column terms are (n+1)!.
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EXAMPLE
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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)
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PROGRAM
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(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 (mathar(AT)strw.leidenuniv.nl), May 19 2006
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CROSSREFS
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Cf. A112357.
Sequence in context: A078937 A167560 A132159 this_sequence A135885 A162312 A141715
Adjacent sequences: A112353 A112354 A112355 this_sequence A112357 A112358 A112359
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 05 2005
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EXTENSIONS
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More terms from Mandy Stoner (astoner(AT)ashland.edu), Apr 27 2006
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