OFFSET
1,1
FORMULA
Equals 2 / pFq(1,1; 3/2,3; -1/2) where pFq() is the generalized hypergeometric function.
Equals 2 / Sum_{k>=0} (-1)^k/binomial(k+2,2)/(2*k+1)!! = 2 / (1 - 1/9 + 1/90 - 1/1050 + 1/14175 - 1/218295 + ... ).
EXAMPLE
2.224412437956340467163837541384021939...
MATHEMATICA
First[RealDigits[2/HypergeometricPFQ[{1, 1}, {3/2, 3}, -1/2], 10, 100]] (* or *)
First[RealDigits[2/Sum[(-1)^k/Binomial[k+2, 2]/(2*k+1)!!, {k, 0, Infinity}], 10, 100]] (* Paolo Xausa, Nov 18 2024 *)
PROG
(PARI)
N=50;
doblfac(n) = if(n<0, 0, n<2, 1, n*doblfac(n-2));
ap1 = 2 / sum(k=0, N, (-1)^k/binomial(k+2, 2)/doblfac(2*k+1));
ap2 = 2 / sum(k=0, N+1, (-1)^k/binomial(k+2, 2)/doblfac(2*k+1));
n = 0; while(digits(floor(10^(n+1)*ap1)) == digits(floor(10^(n+1)*ap2)), n++);
A367120 = digits(floor(10^n*ap1));
CROSSREFS
KEYWORD
AUTHOR
Rok Cestnik, Nov 13 2023
STATUS
approved