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 A100622 #25 Jan 25 2018 04:58:57
%S A100622 1,1,2,10,94,1286,22876,499612,12925340,386356924,13099953016,
%T A100622 496719289496,20825694943912,956599393819720,47772070664027984,
%U A100622 2577034852683364816,149335440671982405136,9251650217381166689552,610194993478502245703200,42688019374465782644235424
%N A100622 Expansion of e.g.f. exp( (1+2*x-sqrt(1-4*x))/4).
%C A100622 Number of topologically distinct solutions to the clone ordering problem for n clones.
%H A100622 Lee A. Newberg, <a href="/A100622/b100622.txt">Table of n, a(n) for n = 0..100</a>
%H A100622 Lee Aaron Newberg, <a href="http://cs.rpi.edu/~leen/publications/NewbergPhD.pdf">Finding, Evaluating and Counting DNA Physical Maps</a>, Ph.D. Thesis, University of California, 1993, Berkeley, CA.
%H A100622 Lee A. Newberg, <a href="https://doi.org/10.1016/0166-218X(96)00093-5">The Number of Clone Orderings</a>, Discrete Applied Mathematics, Vol. 69 (1996) pp. 233-245.
%F A100622 a(n) = n! for n = 0, 1, 2. a(n) = (4n-5) * a(n-1) - (4n-7) * a(n-2) + (n-2) * a(n-3) for n > 2. - _Lee A. Newberg_, Oct 18 2006
%F A100622 a(n) ~ n^(n-1)*exp(3/8-n)*2^(2*n-5/2). - _Vaclav Kotesovec_, Jun 26 2013
%F A100622 Given e.g.f. A(x), then A'(x) / A(x) = g.f. for A088218. - _Michael Somos_, Jan 03 2015
%F A100622 E.g.f.: exp( (1 + 2*x - sqrt(1 - 4*x)) / 4). - _Michael Somos_, Jan 03 2015
%F A100622 0 = a(n)*(+a(n+1) - 5*a(n+2) + 7*a(n+3) - a(n+4)) + a(n+1)*(-3*a(n+1) + 17*a(n+2) - 23*a(n+3) + 4*a(n+4)) + a(n+2)*(-8*a(n+2) + 12*a(n+3) - 4*a(n+4)) + a(n+3)*(+4*a(n+3)) for all n>-2. - _Michael Somos_, Jan 03 2015
%e A100622 G.f. = 1 + x + 2*x^2 + 10*x^3 + 94*x^4 + 1286*x^5 + 22876*x^6 + 499612*x^7 + ...
%p A100622 a := proc(n) option remember: if n = 0 then factorial(0) elif n = 1 then factorial(1) elif n = 2 then factorial(2) elif n >= 3 then (4*n-5)*procname(n-1) - (4*n-7)*procname(n-2) + (n-2)*procname(n-3) fi; end:
%p A100622 seq(a(n), n = 0..250); # _Muniru A Asiru_, Jan 23 2018
%t A100622 CoefficientList[Series[Exp[(1+2*x-Sqrt[1-4*x])/4], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 26 2013 *)
%o A100622 (PARI) {a(n) = if( n<0, 0, n! * polcoeff( exp( (1 + 2*x - sqrt(1 - 4*x + x * O(x^n))) / 4), n))}; /* _Michael Somos_, Jan 03 2015 */
%Y A100622 E.g.f. (1+2*x-sqrt(1-4*x))/4 gives A000407.
%Y A100622 Cf. A088218.
%K A100622 nonn
%O A100622 0,3
%A A100622 _N. J. A. Sloane_, Dec 04 2004