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.
%I A320961 #11 Jul 21 2019 04:22:26 %S A320961 1,1,4,27,353,6128,145159,4402407,166608593,7666343436,420646243820, %T A320961 27079750092637,2018074017351900,172131994564410026, %U A320961 16641769389384512884,1808431867178308597550,219272140061011055068448,29473880023661693302772550,4366902281695075479226089449 %N A320961 The exponential limit of (-x)!, rounded to the nearest integer. %C A320961 The exponential limit of a function is defined in A320956. Applied to (-x)! Maple returns a sequence of sums of Zeta values, powers of Pi, powers of Euler's gamma, etc.. The sequence starts: 1, gamma, (1/3)*Pi^2 + 2* gamma^2, 10*Zeta(3) + (5/2)*Pi^2*gamma + 5*gamma^3, ... These sums, rounded to the nearest integer, give the sequence. %p A320961 explim := (len, f) -> seq(combinat:-bell(n)*((D@@n)(f))(0), n=0..len): %p A320961 explim(18, x -> (-x)!): map(round, [evalf(%, 46)]); %t A320961 m = 19; CoefficientList[(-x)!+O[x]^m, x]*Range[0, m-1]!*BellB[Range[0, m-1]] // Round (* _Jean-François Alcover_, Jul 21 2019 *) %Y A320961 Cf. A320956, A000142. %Y A320961 The exponential limit of other functions: A320955 (exp), A320962 (log(x+1)), A320958 (arcsin), A320959 (arctanh). %K A320961 nonn %O A320961 0,3 %A A320961 _Peter Luschny_, Nov 07 2018