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 A178343 Triangle T(n,m)= binomial(n, m)/Beta(m + 1, n - m + 1) read by rows. 0
 1, 2, 2, 3, 12, 3, 4, 36, 36, 4, 5, 80, 180, 80, 5, 6, 150, 600, 600, 150, 6, 7, 252, 1575, 2800, 1575, 252, 7, 8, 392, 3528, 9800, 9800, 3528, 392, 8, 9, 576, 7056, 28224, 44100, 28224, 7056, 576, 9, 10, 810, 12960, 70560, 158760, 158760, 70560, 12960, 810, 10 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Beta(x,y) = Gamma(x)*Gamma(y)/Gamma(x+y) is the Beta-function. Row sums are A037965(n+1). The second column is A011379. LINKS FORMULA T(n,m)=T(n,n-m) = (n+1)*( binomial(n,m))^2 = (n+1)*A008459(n). EXAMPLE 1; 2, 2; 3, 12, 3; 4, 36, 36, 4; 5, 80, 180, 80, 5; 6, 150, 600, 600, 150, 6; 7, 252, 1575, 2800, 1575, 252, 7; 8, 392, 3528, 9800, 9800, 3528, 392, 8; 9, 576, 7056, 28224, 44100, 28224, 7056, 576, 9; 10, 810, 12960, 70560, 158760, 158760, 70560, 12960, 810, 10; 11, 1100, 22275, 158400, 485100, 698544, 485100, 158400, 22275, 1100, 11; MATHEMATICA Flatten[Table[Table[Binomial[n, m]/Beta[m + 1, n - m + 1], {m, 0, n}], {n, 0, 10}]] CROSSREFS Cf. A037965 Sequence in context: A265783 A246670 A075095 * A156136 A134243 A182779 Adjacent sequences:  A178340 A178341 A178342 * A178344 A178345 A178346 KEYWORD nonn,easy,tabl AUTHOR Roger L. Bagula, May 25 2010 EXTENSIONS Edited by the Assoc. Eds. of the OEIS - Jun 27 2010 STATUS approved

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Last modified September 17 22:53 EDT 2019. Contains 327147 sequences. (Running on oeis4.)