A273878 Numerator of (2*(n+1)!/(n+2)).

1, 4, 3, 48, 40, 1440, 1260, 8960, 72576, 7257600, 6652800, 958003200, 889574400, 11623772160, 163459296000, 41845579776000, 39520825344000, 12804747411456000, 12164510040883200, 231704953159680000, 4644631106519040000, 2248001455555215360000, 2154334728240414720000

Offset

0,2

Comments

The moments, i.e., E(X^n) = Integral_{x=0..oo} x^n*p(x) dx for n > 0, of the probability density function p(x) = 2*x*E(x, 1, 1), see A163931, lead to this sequence.

Links

Table of n, a(n) for n=0..22.

J. W. Meijer and N. H. G. Baken, The Exponential Integral Distribution, Statistics and Probability Letters, Volume 5, No.3, April 1987. pp 209-211.

Formula

a(n) = numerator(2*(n+1)!/(n+2)).

a(n) = (n+1) * A090586(n+1).

a(2*n) = A110468(n) and a(2*n+1) = (2*n)!*A085250(n+1)/A128060(n+2).

Example

The first few moments of p(x) are: 1, 4/3, 3, 48/5, 40, 1440/7, ...

Maple

a := proc(n): numer(2*(n+1)!/(n+2)) end: seq(a(n), n=0..20);

Prog

(PARI) a(n) = numerator(2*(n+1)!/(n+2)) \\ Felix Fröhlich, Jun 09 2016

Crossrefs

Cf. A090585 (denominators), A090586, A085250, A110468, A128059, A128060, A163931.

Sequence in context: A324671 A249226 A328193 * A013335 A298314 A299389

Adjacent sequences: A273875 A273876 A273877 * A273879 A273880 A273881

Keyword

nonn,frac,easy

Author

Johannes W. Meijer, Jun 08 2016

Extensions

a(21)-a(22) from Stefano Spezia, Jun 03 2026

Status

approved