A377188 Triangle read by rows: T(n,k) = denominator((n^2 + k)/(n^2 - k)).

1, 7, 1, 7, 13, 3, 23, 11, 21, 2, 17, 11, 4, 31, 5, 47, 23, 45, 22, 43, 3, 31, 61, 15, 59, 29, 57, 7, 79, 13, 77, 38, 25, 37, 73, 4, 49, 97, 12, 19, 47, 93, 23, 91, 9, 119, 59, 117, 58, 115, 57, 113, 56, 111, 5, 71, 47, 35, 139, 23, 137, 17, 15, 67, 133, 11

Offset

2,2

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, Section 1.3, p. 14.

Links

Table of n, a(n) for n=2..67.

Formula

Limit_{n->oo} Product_{k=1..n} A377187(n,k)/T(n,k) = e = A001113 (see Finch).

T(n,n) = A026741(n-1).

Example

The triangle begins as:
   1;
   7,  1;
   7, 13,  3;
  23, 11, 21,  2;
  17, 11,  4, 31,  5;
  47, 23, 45, 22, 43,  3;
  31, 61, 15, 59, 29, 57,  7;
  79, 13, 77, 38, 25, 37, 73,  4;
  49, 97, 12, 19, 47, 93, 23, 91, 9;
  ...

Mathematica

T[n_, k_]:=Denominator[(n^2+k)/(n^2-k)]; Table[T[n, k], {n, 2, 12}, {k, 2, n}]//Flatten

Prog

(Python)
from math import isqrt, comb, gcd
def A377188(n): return (d:=(a:=(m:=isqrt(k:=n-1<<1))+(k>m*(m+1))+1)**2-(b:=n-comb(a-1, 2)))//gcd(d, d+(b<<1)) # Chai Wah Wu, Nov 12 2024

Crossrefs

Cf. A001113, A026741, A377187 (numerator).

Sequence in context: A093564 A081776 A354128 * A256255 A131115 A151778

Adjacent sequences: A377185 A377186 A377187 * A377189 A377190 A377191

Keyword

nonn,easy,frac,tabl

Author

Stefano Spezia, Oct 19 2024

Status

approved