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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = A000217(A072643(n)).
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
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):
seq(T(n), n=0..5); # Alois P. Heinz, Feb 16 2024
MATHEMATICA
Flatten[Array[Table[PolygonalNumber[#], CatalanNumber[#]] &, 7, 0]]
CROSSREFS
Row sums of A370221 (for n >= 1).
Row sums as triangle give A002457(n-1) for n>=1.
Sequence in context: A342511 A175520 A271668 * A072464 A262871 A160745
KEYWORD
nonn,easy,tabf
AUTHOR
Paolo Xausa, Feb 14 2024
STATUS
approved

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Last modified June 17 07:23 EDT 2024. Contains 373433 sequences. (Running on oeis4.)