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%I M1493 #33 Nov 17 2022 07:20:47
%S 1,2,5,16,62,276,1377,7596,45789,298626,2090910,15621640,123897413,
%T 1038535174,9165475893,84886111212,822648571314,8321077557124,
%U 87648445601429,959450073912136,10894692556576613,128114221270929646
%N Number of partitional matroids on n elements.
%D Recski, A.; Enumerating partitional matroids. Stud. Sci. Math. Hungar. 9 (1974), 247-249 (1975).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A005387/b005387.txt">Table of n, a(n) for n = 0..100</a>
%H A. Recski, <a href="/A005387/a005387_1.pdf">Enumerating partitional matroids</a>, Preprint.
%H A. Recski & N. J. A. Sloane, <a href="/A005387/a005387.pdf">Correspondence, 1975</a>
%H <a href="/index/Mat#matroid">Index entries for sequences related to matroids</a>
%F E.g.f.: exp( (x-1)*exp(x) + 2*x + 1 ).
%F a(n) = Sum_{j=0..n} binomial(n, j) * 2^(n-j) * A327006(j+1). - _G. C. Greubel_, Nov 16 2022
%t With[{nn=30},CoefficientList[Series[Exp[(x-1)E^x+2x+1],{x,0,nn}],x]Range[0,nn]!] (* _Harvey P. Dale_, Nov 22 2012 *)
%o (Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!(Laplace( Exp((x-1)*Exp(x) + 2*x + 1) ))); // _G. C. Greubel_, Nov 16 2022
%o (SageMath)
%o def A005387_list(prec):
%o P.<x> = PowerSeriesRing(QQ, prec)
%o return P( exp((x-1)*exp(x) + 2*x + 1) ).egf_to_ogf().list()
%o A005387_list(40) # _G. C. Greubel_, Nov 16 2022
%Y Cf. A327006.
%K nonn,easy,nice
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _James A. Sellers_, Aug 21 2000
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