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%I #35 May 13 2022 16:10:52
%S 1,2,9,112,2921,126966,8204497,735944084,87394386417,13265365173706,
%T 2504688393449081,575664638548522392,158222202503521622809,
%U 51242608446417388426622,19312113111034490954560641,8379247307752508262094697596,4146836850351947542340780899937
%N Number of strings on n symbols in Stockhausen problem.
%H G. C. Greubel, <a href="/A008269/b008269.txt">Table of n, a(n) for n = 0..235</a>
%H R. C. Read, <a href="http://dx.doi.org/10.1016/S0012-365X(96)00255-5">Combinatorial problems in theory of music</a>, Discrete Math. 167 (1997), 543-551.
%H Ronald C. Read, Lily Yen, <a href="https://doi.org/10.1006/jcta.1996.0085">A note on the Stockhausen problem</a>, J. Comb. Theory, Ser. A 76, No. 1, 1-10.
%F a(n) = (2*n^2-5*n+4)*a(n-1) + (-4*n^2+15*n-14)*a(n-2) + (2*n^2-10*n+12)*a(n-3).
%F a(n) = hypergeom([1, 1/2, -n], [], -2). - _Vladeta Jovovic_, Apr 08 2007
%F a(n) = (1/2^n) * Integral_{x>=0} (2+x^2)^n*exp(-x) dx. - _Gerald McGarvey_, Oct 12 2007
%F a(n) ~ sqrt(Pi) * 2^(n+1) * n^(2*n+1/2) / exp(2*n). - _Vaclav Kotesovec_, Feb 18 2015
%F a(n) = Sum_{i=0..n} binomial(n,i) * A000680(i). - _Håvar Andre Melheim Salbu_, May 13 2022
%t Table[HypergeometricPFQ[{1,1/2,-n},{},-2],{n,0,20}] (* _Vaclav Kotesovec_, Feb 18 2015 *)
%o (PARI) for(n=0,14,print1(2^(-n)*round(intnum(x=0,999,(2+x^2)^n*exp(-x))),", ")) \\ _Gerald McGarvey_, Oct 12 2007
%o (PARI) a(n) = sum(i=0, n, binomial(n,i) * (2*i)!/2^i); \\ _Michel Marcus_, May 13 2022
%Y Cf. A000680.
%K nonn
%O 0,2
%A _Lily Yen_
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