This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A226078 #28 Nov 28 2024 20:33:28
%S A226078 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,
%T A226078 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,
%U A226078 17,19,23,16,9,5,17,19,23,29,2,9,5,17,19,23,29,31
%N A226078 Table read by rows: prime power factors of central binomial coefficients, cf. A000984.
%H A226078 Reinhard Zumkeller, <a href="/A226078/b226078.txt">Rows n = 0..250 of triangle, flattened</a>
%F A226078 T(n,k) = A141809(A000984(n),k) for k = 0..A067434(n)-1.
%e A226078 . n initial rows A000984(n) A226047(n)
%e A226078 . ---+------------------------------+-------------+------------
%e A226078 . 0 [1] 1
%e A226078 . 1 [2] 2 2
%e A226078 . 2 [2,3] 6 3
%e A226078 . 3 [4,5] 20 5
%e A226078 . 4 [2,5,7] 70 7
%e A226078 . 5 [4,9,7] 252 9
%e A226078 . 6 [4,3,7,11] 924 11
%e A226078 . 7 [8,3,11,13] 3432 13
%e A226078 . 8 [2,9,5,11,13] 12870 13
%e A226078 . 9 [4,5,11,13,17] 48620 17
%e A226078 . 10 [4,11,13,17,19] 184756 19
%e A226078 . 11 [8,3,7,13,17,19] 705432 19
%e A226078 . 12 [4,7,13,17,19,23] 2704156 23
%e A226078 . 13 [8,25,7,17,19,23] 10400600 25
%e A226078 . 14 [8,27,25,17,19,23] 40116600 27
%e A226078 . 15 [16,9,5,17,19,23,29] 155117520 29
%e A226078 . 16 [2,9,5,17,19,23,29,31] 601080390 31
%e A226078 . 17 [4,27,5,11,19,23,29,31] 2333606220 31
%e A226078 . 18 [4,3,25,7,11,19,23,29,31] 9075135300 31
%e A226078 . 19 [8,3,25,7,11,23,29,31,37] 35345263800 37
%e A226078 . 20 [4,9,5,7,11,13,23,29,31,37] 137846528820 37 .
%p A226078 f:= n-> add(i[2]*x^i[1], i=ifactors(n)[2]):
%p A226078 b:= proc(n) local p;
%p A226078 p:= add(f(n+i) -f(i), i=1..n);
%p A226078 seq(`if`(coeff(p, x, i)>0,
%p A226078 i^coeff(p, x, i), NULL), i=1..degree(p))
%p A226078 end:
%p A226078 T:= n-> `if`(n=0, 1, b(n)):
%p A226078 seq(T(n), n=0..30); # _Alois P. Heinz_, May 25 2013
%t A226078 Table[Power @@@ FactorInteger[(2n)!/n!^2] , {n, 0, 30}] // Flatten (* _Jean-François Alcover_, Jul 29 2015 *)
%o A226078 (Haskell)
%o A226078 a226078 n k = a226078_tabf !! n !! k
%o A226078 a226078_row n = a226078_tabf !! n
%o A226078 a226078_tabf = map a141809_row a000984_list
%o A226078 (PARI) row(n)= if(n<1, [1], [ e[1]^e[2] |e<-Col(factor(binomial(2*n, n)))]); \\ _Ruud H.G. van Tol_, Nov 18 2024
%Y A226078 Cf. A067434 (row lengths), A001316 (left edge), A060308 (right edge), A226047 (row maxima), A226083 (row minima), A000984 (row products).
%Y A226078 Cf. A267823.
%K A226078 nonn,tabf,look
%O A226078 0,2
%A A226078 _Reinhard Zumkeller_, May 25 2013