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Search: id:A121757
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| A121757 |
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Triangle read by rows: multiply Pascal's triangle by 1,2,6,24,120,720,... = A000142. |
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+0
2
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| 1, 1, 2, 1, 4, 6, 1, 6, 18, 24, 1, 8, 36, 96, 120, 1, 10, 60, 240, 600, 720, 1, 12, 90, 480, 1800, 4320, 5040, 1, 14, 126, 840, 4200, 15120, 35280, 40320, 1, 16, 168, 1344, 8400, 40320, 141120, 322560, 362880, 1, 18, 216, 2016, 15120, 90720, 423360, 1451520
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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Row sums are 1,3,11,49,261,1631,... = A001339
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FORMULA
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a(n,k)=A007318(n,k)*A000142(k+1), k=0,1,..,n, n=0,1,2,3... - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 02 2006
a(n,k) = A008279(n,k) * (k+1). a(n,k) = n!*(k+1)/(n-k)!. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 20 2006
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EXAMPLE
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Row 6 is 1*1 5*2 10*6 10*24 5*120 1*720
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PROGRAM
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(PARI) A000142(n)={ return(n!) ; } A007318(n, k)={ return(binomial(n, k)) ; } A121757(n, k)={ return(A007318(n, k)*A000142(k+1)) ; } { for(n=0, 12, for(k=0, n, print1(A121757(n, k), ", ") ; ); ) ; } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 02 2006
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CROSSREFS
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Cf. A007526 A000522.
Cf. A008279.
Sequence in context: A033877 A059369 A098473 this_sequence A109822 A114192 A114656
Adjacent sequences: A121754 A121755 A121756 this_sequence A121758 A121759 A121760
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Alford Arnold (Alford1940(AT)aol.com), Aug 19 2006
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 02 2006
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