A226078 - OEIS

A226078

Table read by rows: prime power factors of central binomial coefficients, cf. A000984.

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

LINKS

Reinhard Zumkeller, Rows n = 0..250 of triangle, flattened

FORMULA

T(n,k) = A141809(A000984(n),k) for k = 0..A067434(n)-1.

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: A328628 A328629 A342022 * A065648 A305977 A329048

Adjacent sequences: A226075 A226076 A226077 * A226079 A226080 A226081

KEYWORD

nonn,tabf,look,changed

AUTHOR

Reinhard Zumkeller, May 25 2013

STATUS

approved