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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-Fran├žois 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 A167506 A072813

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 February 22 03:55 EST 2018. Contains 299428 sequences. (Running on oeis4.)