

A370291


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


2



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
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OFFSET

0,3


LINKS



FORMULA

Sum_{n>=1} (1)^(n+1)/a(n) = Sum_{n>=1} (1/2)^(n1)/(2^n1) = 0.86233289403022175171... .  Amiram Eldar, Feb 17 2024


EXAMPLE

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;
...


MAPLE

T:= n> n*(n+1)/2$binomial(2*n, n)/(n+1):


MATHEMATICA

Flatten[Array[Table[PolygonalNumber[#], CatalanNumber[#]] &, 7, 0]]


CROSSREFS

Row sums as triangle give A002457(n1) for n>=1.


KEYWORD

nonn,easy,tabf


AUTHOR



STATUS

approved



