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 A226078 Table read by rows: prime power factors of central binomial coefficients, cf. A000984. 9
 1, 2, 2, 3, 4, 5, 2, 5, 7, 4, 9, 7, 4, 3, 7, 11, 8, 3, 11, 13, 2, 9, 5, 11, 13, 4, 5, 11, 13, 17, 4, 11, 13, 17, 19, 8, 3, 7, 13, 17, 19, 4, 7, 13, 17, 19, 23, 8, 25, 7, 17, 19, 23, 8, 27, 25, 17, 19, 23, 16, 9, 5, 17, 19, 23, 29, 2, 9, 5, 17, 19, 23, 29, 31 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS T(n,k) = A141809(A000984(n)),k) for k = 0..A067434(n)-1. LINKS Reinhard Zumkeller, Rows n = 0..250 of triangle, flattened EXAMPLE .   n        initial rows               A000984(n)   A226047(n) .  ---+------------------------------+-------------+------------ .   0   [1]                                      1 .   1   [2]                                      2            2 .   2   [2,3]                                    6            3 .   3   [4,5]                                   20            5 .   4   [2,5,7]                                 70            7 .   5   [4,9,7]                                252            9 .   6   [4,3,7,11]                             924           11 .   7   [8,3,11,13]                           3432           13 .   8   [2,9,5,11,13]                        12870           13 .   9   [4,5,11,13,17]                       48620           17 .  10   [4,11,13,17,19]                     184756           19 .  11   [8,3,7,13,17,19]                    705432           19 .  12   [4,7,13,17,19,23]                  2704156           23 .  13   [8,25,7,17,19,23]                 10400600           25 .  14   [8,27,25,17,19,23]                40116600           27 .  15   [16,9,5,17,19,23,29]             155117520           29 .  16   [2,9,5,17,19,23,29,31]           601080390           31 .  17   [4,27,5,11,19,23,29,31]         2333606220           31 .  18   [4,3,25,7,11,19,23,29,31]       9075135300           31 .  19   [8,3,25,7,11,23,29,31,37]      35345263800           37 .  20   [4,9,5,7,11,13,23,29,31,37]   137846528820           37 . MAPLE f:= n-> add(i[2]*x^i[1], i=ifactors(n)[2]): b:= proc(n) local p;       p:= add(f(n+i) -f(i), i=1..n);       seq(`if`(coeff(p, x, i)>0,              i^coeff(p, x, i), NULL), i=1..degree(p))     end: T:= n-> `if`(n=0, 1, b(n)): seq(T(n), n=0..30);  # Alois P. Heinz, May 25 2013 MATHEMATICA Table[Power @@@ FactorInteger[(2n)!/n!^2] , {n, 0, 30}] // Flatten (* Jean-François Alcover, Jul 29 2015 *) PROG (Haskell) a226078 n k = a226078_tabf !! n !! k a226078_row n = a226078_tabf !! n a226078_tabf = map a141809_row a000984_list CROSSREFS Cf. A067434 (row lengths), A001316 (left edge), A060308 (right edge), A226047 (row maxima), A226083 (row minima), A000984 (row products). Cf. A267823. Sequence in context: A036809 A111263 A286626 * A065648 A305977 A167506 Adjacent sequences:  A226075 A226076 A226077 * A226079 A226080 A226081 KEYWORD nonn,tabf,look AUTHOR Reinhard Zumkeller, May 25 2013 STATUS approved

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Last modified October 23 12:04 EDT 2019. Contains 328345 sequences. (Running on oeis4.)