Search: id:A107430
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%I A107430
%S A107430 1,1,1,1,1,2,1,1,3,3,1,1,4,4,6,1,1,5,5,10,10,1,1,6,6,15,15,20,1,1,7,7,
%T A107430 21,21,35,35,1,1,8,8,28,28,56,56,70,1,1,9,9,36,36,84,84,126,126,1,1,10,
%U A107430 10,45,45,120,120,210,210,252,1,1,11,11,55,55,165,165,330,330,462,462,
               1
%N A107430 Triangle read by rows: row n is row n of Pascal's triangle (A007318) 
               sorted into increasing order.
%C A107430 Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 28 2008: 
               (Start)
%C A107430 By rows = partial sums of A053121 rows, then reverse. Example:
%C A107430 Row 4 of A053121 = (2, 0, 3, 0, 1), then -> (6, 4, 4, 1, 1) -> (1, 1, 
               4, 4, 6). (End)
%F A107430 T(n,k) = C(n,floor(k/2)). - Paul Barry (pbarry(AT)wit.ie), Dec 15 2006; 
               corrected by Philippe DELEHAM, Mar 15 2007
%F A107430 Sum_{k, 0<=k<=n}T(n,k)*x^(n-k) = A127363(n), A127362(n), A127361(n), 
               A126869(n), A001405(n), A000079(n), A127358(n), A127359(n), A127360(n)for 
               n=-4,-3,-2,-1,0,1,2,3,4 respectively . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Mar 29 2007
%e A107430 Triangle begins:
%e A107430 1;
%e A107430 1,1;
%e A107430 1,1,2;
%e A107430 1,1,3,3;
%e A107430 1,1,4,4,6;
%p A107430 for n from 0 to 10 do sort([seq(binomial(n,k),k=0..n)]) od;# yields sequence 
               in triangular form (Deustch)
%t A107430 Flatten[ Table[ Sort[ Table[ Binomial[n, k], {k, 0, n}]], {n, 0, 12}]] 
               (from Robert G. Wilson v (rgwv(AT)rgwv.com), May 28 2005)
%Y A107430 A061554 is similar but with rows sorted into decreasing order.
%Y A107430 Cf. A034868.
%Y A107430 A053121 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 28 2008]
%Y A107430 Sequence in context: A049695 A096589 A099573 this_sequence A132892 A077028 
               A114225
%Y A107430 Adjacent sequences: A107427 A107428 A107429 this_sequence A107431 A107432 
               A107433
%K A107430 nonn,tabl,easy
%O A107430 0,6
%A A107430 Philippe DELEHAM, May 21 2005
%E A107430 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu) and Robert 
               G. Wilson v (rgwv(AT)rgwv.com), May 28 2005

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