A370291 Triangular number T(n) = A000217(n) occurs C(n) = A000108(n) times.
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, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 21, 21, 21, 21, 21
Offset: 0
Examples
Written as a triangle: 0; 1; 3, 3; 6, 6, 6, 6, 6; 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10; ...
Links
- Paolo Xausa, Table of n, a(n) for n = 0..10000
Crossrefs
Programs
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Maple
T:= n-> n*(n+1)/2$binomial(2*n,n)/(n+1): seq(T(n), n=0..5); # Alois P. Heinz, Feb 16 2024
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Mathematica
Flatten[Array[Table[PolygonalNumber[#], CatalanNumber[#]] &, 7, 0]]
Formula
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