A381681 a(n) is one of two integer components (with A000254) used in computing the inverse second moment of X+n, where X~Poisson(1).
0, 1, 2, 7, 30, 159, 998, 7251, 59862, 553591, 5669406, 63698427, 779065694, 10304068863, 146547757014, 2230287456259, 36165665815878, 622513383121671, 11336090988469742, 217741030441959051, 4399571340398826126, 93286012779568250767, 2071087588405552461414, 48048511292938827392403
Offset: 0
Keywords
Examples
If X~Poisson(1), then E[(X+n)^(-2)] = (-1)^n * {(n-1)! * [-Ei(1)+gamma] - A000254(n-1) + e*a(n-1)}/e for n = 1,2,... where gamma is Euler's constant.
Links
- Michael R. Powers, Conjunctions of Three "Euler Constants" in Poisson-Related Expressions, arXiv:2503.02054 [math.NT], 2025.
Crossrefs
Programs
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PARI
a(n) = n! * sum(i=1, n, (1/i)*sum(j=0, i-1, (-1)^j/j!)); \\ Michel Marcus, Mar 07 2025
Formula
a(n) = n! * Sum_{i=1..n} (1/i)*Sum_{j=0..i-1} (-1)^j/j!.
Comments