OFFSET
0,2
COMMENTS
E.g.f. A(x)=y satisfies 0=(2x^3+2x^2)y''+(-3x^3+4x-1)y'+(x^3-x^2-2x+3)y. - Michael Somos, Mar 15 2004
Number of ways to use the elements of {1,..,k}, 0<=k<=2n, once each to form a sequence of n (possibly empty) sets, each having at most 2 elements. - Bob Proctor, Apr 18 2005
REFERENCES
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 17.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..230
Robert A. Proctor, Let's Expand Rota's Twelvefold Way For Counting Partitions!, arXiv:math.CO/0606404, Jan 05, 2007
FORMULA
n*a(n) = (2*n^3 - n^2 + n + 1)*a(n-1) + (-3*n^3 + 4*n^2 + 2*n - 3)*a(n-2) + (n^3 - 2*n^2 - n + 2)*a(n-3).
a(n) ~ sqrt(Pi)*2^(n+1)*n^(2*n+1/2)/exp(2*n-1). - Vaclav Kotesovec, Oct 19 2013
MATHEMATICA
Table[nn=2n; a=1+x+x^2/2!; Total[Range[0, nn]!CoefficientList[Series[a^n, {x, 0, nn}], x]], {n, 0, 15}] (* Geoffrey Critzer, Dec 23 2011 *)
PROG
(PARI) a(n)=local(A); if(n<0, 0, A=(1+x+x^2/2)^n; sum(k=0, 2*n, k!*polcoeff(A, k)))
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Aug 18 2002
STATUS
approved