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A002018 From a distribution problem.
(Formerly M3652 N1485)
1
1, 1, 4, 33, 480, 11010, 367560, 16854390, 1016930880, 78124095000, 7446314383200, 862332613342200, 119261328828364800, 19415283189746043600, 3675162134109650184000, 800409618620667941886000, 198730589981586780813696000, 55800304882692417053710704000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

H. Anand, V. C. Dumir and H. Gupta, A combinatorial distribution problem, Duke Math. J., 33 (1996), 757-769.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n) = n*(2*n-1)*b(n) - n*(n-1)^2*b(n-1), b(n) = A000681(n).

MATHEMATICA

b[n_] := Sum[(2i)!*n!^2/(2^i*i!^2*(n-i)!), {i, 0, n}]/2^n; a[n_] := n*(2n-1)*b[n-1] - n*(n-1)^2*b[n-2]; a[0]=1; Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Aug 08 2012, after formula *)

CROSSREFS

Sequence in context: A296835 A002190 A101981 * A219504 A258180 A072754

Adjacent sequences:  A002015 A002016 A002017 * A002019 A002020 A002021

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from David W. Wilson

STATUS

approved

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Last modified December 6 04:14 EST 2019. Contains 329784 sequences. (Running on oeis4.)