cp's OEIS Frontend

A366151 a(n) = T(n, 3), where T(n, k) = Sum_{i=0..n} i^k * binomial(n, i) * (1/2)^(n-k).

%I A366151 #15 Oct 28 2023 09:32:18
%S A366151 0,4,20,54,112,200,324,490,704,972,1300,1694,2160,2704,3332,4050,4864,
%T A366151 5780,6804,7942,9200,10584,12100,13754,15552,17500,19604,21870,24304,
%U A366151 26912,29700,32674,35840,39204,42772,46550
%N A366151 a(n) = T(n, 3), where T(n, k) = Sum_{i=0..n} i^k * binomial(n, i) * (1/2)^(n-k).
%C A366151 A mean of binomials as might occur as the Expectation of random variables.
%F A366151 a(n) = n^2*(n + 3).
%F A366151 a(n) = [x^n] (2*x*(2 + 2*x - x^2))/(x - 1)^4.
%F A366151 a(n) = n! * [x^n] exp(x)*(x^3 + 6*x^2 + 4*x).
%p A366151 a := n -> n^2*(n + 3): seq(a(n), n = 0..35);
%Y A366151 T(n, 0) = A000012; T(n, 1) = A001477; T(n, 2) = A002378; T(n, 3) = this sequence.
%Y A366151 T(1, n) = A011782; T(2, n) = A063376(n) (with offset 0); T(n, n) = A072034(n).
%K A366151 nonn
%O A366151 0,2
%A A366151 _Peter Luschny_, Oct 27 2023