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A377188
Triangle read by rows: T(n,k) = denominator((n^2 + k)/(n^2 - k)).
2
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.
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
KEYWORD
nonn,easy,frac,tabl
AUTHOR
Stefano Spezia, Oct 19 2024
STATUS
approved