A354299 a(n) is the denominator of Sum_{k=1..n} (-1)^(k+1) / (2*k-1)!!.

1, 3, 15, 105, 189, 10395, 135135, 2027025, 34459425, 130945815, 13749310575, 316234143225, 7905853580625, 12556355686875, 1238056670725875, 776918153694375, 6332659870762850625, 7642865361265509375, 8200794532637891559375, 63966197354575554163125, 13113070457687988603440625

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..403

Formula

Denominators of coefficients in expansion of sqrt(Pi*x*exp(-x)/2) * erfi(sqrt(x/2)) / (1 - x).

Example

1, 2/3, 11/15, 76/105, 137/189, 7534/10395, 97943/135135, 1469144/2027025, 24975449/34459425, ...

Maple

S:= 0: R:= NULL:
for n from 1 to 100 do
  S:= S + (-1)^(n+1)/doublefactorial(2*n-1);
  R:= R, denom(S);
od:
R; # Robert Israel, Jan 10 2024

Mathematica

Table[Sum[(-1)^(k + 1)/(2 k - 1)!!, {k, 1, n}], {n, 1, 21}] // Denominator
nmax = 21; CoefficientList[Series[Sqrt[Pi x Exp[-x]/2] Erfi[Sqrt[x/2]]/(1 - x), {x, 0, nmax}], x] // Denominator // Rest
Table[1/(1 + ContinuedFractionK[2 k - 1, 2 k, {k, 1, n - 1}]), {n, 1, 21}] // Denominator

Crossrefs

Cf. A001147, A053556, A061355, A064647, A113013, A143383, A289488, A306858, A354298 (numerators).

Sequence in context: A181131 A359417 A359418 * A293996 A229726 A145624

Adjacent sequences: A354296 A354297 A354298 * A354300 A354301 A354302

Keyword

nonn,frac

Author

Ilya Gutkovskiy, May 23 2022

Status

approved