cp's OEIS Frontend

A370291 Triangular number T(n) = A000217(n) occurs C(n) = A000108(n) times.

%I A370291 #21 Feb 17 2024 04:04:27
%S A370291 0,1,3,3,6,6,6,6,6,10,10,10,10,10,10,10,10,10,10,10,10,10,10,15,15,15,
%T A370291 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,
%U A370291 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,21,21,21,21,21
%N A370291 Triangular number T(n) = A000217(n) occurs C(n) = A000108(n) times.
%H A370291 Paolo Xausa, <a href="/A370291/b370291.txt">Table of n, a(n) for n = 0..10000</a>
%F A370291 a(n) = A000217(A072643(n)).
%F A370291 Sum_{n>=1} (-1)^(n+1)/a(n) = Sum_{n>=1} (-1/2)^(n-1)/(2^n-1) = 0.86233289403022175171... . - _Amiram Eldar_, Feb 17 2024
%e A370291 Written as a triangle:
%e A370291    0;
%e A370291    1;
%e A370291    3,  3;
%e A370291    6,  6,  6,  6,  6;
%e A370291   10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10;
%e A370291   ...
%p A370291 T:= n-> n*(n+1)/2$binomial(2*n,n)/(n+1):
%p A370291 seq(T(n), n=0..5);  # _Alois P. Heinz_, Feb 16 2024
%t A370291 Flatten[Array[Table[PolygonalNumber[#], CatalanNumber[#]] &, 7, 0]]
%Y A370291 Cf. A000108, A000217, A072643.
%Y A370291 Row sums of A370221 (for n >= 1).
%Y A370291 Row sums as triangle give A002457(n-1) for n>=1.
%K A370291 nonn,easy,tabf
%O A370291 0,3
%A A370291 _Paolo Xausa_, Feb 14 2024