A081418 - OEIS

%I #11 Aug 23 2024 21:06:10

%S 1,1,1,1,1,1,1,1,2,1,1,1,2,1,1,1,1,3,3,3,1,1,1,3,3,3,1,1,1,1,4,6,6,4,

%T 4,1,1,1,4,6,6,4,4,1,1,1,1,4,6,6,4,4,1,1,1,1,1,4,6,6,4,4,1,1,1,1,1,1,

%U 5,10,10,10,10,5,5,5,5,1,1,1,5,10,10,10,10,5,5,5,5,1,1,1,1,6,15,15,20,20,15,15,15,15,6,6,1

%N A000720 applied to Pascal-triangle as follows: C(pi(n),pi(j)), j=0..n and n=0,1,2,...

%e Triangle begins:

%e 1,

%e 1,1,

%e 1,1,1,

%e 1,1,2,1,

%e 1,1,2,1,1,

%e 1,1,3,3,3,1,

%e 1,1,3,3,3,1,1,

%e 1,1,4,6,6,4,4,1,

%e 1,1,4,6,6,4,4,1,1,

%e 1,1,4,6,6,4,4,1,1,1,

%e 1,1,4,6,6,4,4,1,1,1,1,

%e 1,1,5,10,10,10,10,5,5,5,5,1,

%e 1,1,5,10,10,10,10,5,5,5,5,1,1,

%e 1,1,6,15,15,20,20,15,15,15,15,6,6,1,

%e 1,1,6,15,15,20,20,15,15,15,15,6,6,1,1,

%e 1,1,6,15,15,20,20,15,15,15,15,6,6,1,1,1

%e Rows are usually asymmetric; 25th row:

%e {1,1,9,36,36,84,84,126,126,126,126,126,126,84,84,84,84,36,36,9,9,9,9,1,1,1}

%t Flatten[Table[Table[Binomial[PrimePi[n], Prime[j]],

%t {j, 0, n}], {n, 0, 15}], 1]

%Y Cf. A000720, A007318, A081417.

%K nonn,tabl

%O 0,9

%A _Labos Elemer_, Apr 02 2003