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.

A053491 Expansion of e.g.f. (1-2*x)^(-x).

This page as a plain text file.
%I A053491 #19 May 21 2022 08:40:59
%S A053491 1,0,4,12,112,960,10848,141120,2122496,36094464,685578240,14385761280,
%T A053491 330532435968,8253827112960,222587077558272,6447285982126080,
%U A053491 199630453605335040,6580280144225894400,230056747973625249792,8503148524089755566080
%N A053491 Expansion of e.g.f. (1-2*x)^(-x).
%H A053491 G. C. Greubel, <a href="/A053491/b053491.txt">Table of n, a(n) for n = 0..400</a>
%F A053491 a(n) ~ 2^(n+1/2)*n^n/exp(n). - _Vaclav Kotesovec_, Jun 27 2013
%F A053491 a(n) = n! * Sum_{k=0..floor(n/2)} 2^(n-k) * |Stirling1(n-k,k)|/(n-k)!. - _Seiichi Manyama_, May 20 2022
%t A053491 CoefficientList[Series[(1-2x)^(-x), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 27 2013 *)
%o A053491 (PARI) a(n) = n!*sum(k=0, n\2, 2^(n-k)*abs(stirling(n-k, k, 1))/(n-k)!); \\ _Seiichi Manyama_, May 20 2022
%Y A053491 Cf. A007113, A053489, A066166.
%K A053491 nonn
%O A053491 0,3
%A A053491 _N. J. A. Sloane_, Jan 15 2000