cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A376922 Variance of n-th power of a standard normal random variable.

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%I A376922 #15 Oct 31 2024 01:48:41
%S A376922 1,2,15,96,945,10170,135135,2016000,34459425,653836050,13749310575,
%T A376922 316126087200,7905853580625,213439785208650,6190283353629375,
%U A376922 191894675132160000,6332659870762850625,221641908024728441250,8200794532637891559375,319830558102716120460000
%N A376922 Variance of n-th power of a standard normal random variable.
%C A376922 The variance of the n-th sample moment is exactly a(n) / k for sample size k.
%C A376922 For a non-standard normal r.v. X ~ N(0, sigma^2), Var(X^n) = a(n) sigma^(2n).
%D A376922 M. G. Kendall and A. Stuart, The Advanced Theory of Statistics Volume 1, Charles Griffin & Company, 1963, page 229.
%F A376922 a(n) = M(2n) - M(n)^2, where M(n) = A123023(n) are the moments of N(0, 1).
%e A376922 If Z ~ N(0, 1), then Var(Z) = 1, Var(Z^2) = 2, Var(Z^3) = 15, etc.
%Y A376922 Cf. A001147, A103639, A123023.
%K A376922 nonn
%O A376922 1,2
%A A376922 _Adam M. Scherlis_, Oct 10 2024