A005387 Number of partitional matroids on n elements.

1, 2, 5, 16, 62, 276, 1377, 7596, 45789, 298626, 2090910, 15621640, 123897413, 1038535174, 9165475893, 84886111212, 822648571314, 8321077557124, 87648445601429, 959450073912136, 10894692556576613, 128114221270929646

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

References

• Recski, A.; Enumerating partitional matroids. Stud. Sci. Math. Hungar. 9 (1974), 247-249 (1975).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 0..100
• A. Recski, Enumerating partitional matroids, Preprint.
• A. Recski & N. J. A. Sloane, Correspondence, 1975
• Index entries for sequences related to matroids

Crossrefs

Cf. A327006.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 40); Coefficients(R!(Laplace( Exp((x-1)*Exp(x) + 2*x + 1) ))); // G. C. Greubel, Nov 16 2022

Mathematica

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 *)

SageMath

def A005387_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( exp((x-1)*exp(x) + 2*x + 1) ).egf_to_ogf().list()
A005387_list(40) # G. C. Greubel, Nov 16 2022

Formula

E.g.f.: exp( (x-1)*exp(x) + 2*x + 1 ).

a(n) = Sum_{j=0..n} binomial(n, j) * 2^(n-j) * A327006(j+1). - G. C. Greubel, Nov 16 2022

Extensions

More terms from James Sellers, Aug 21 2000