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0, 2, 8, 24, 64, 160, 384, 896, 2048, 4608, 10240, 22528, 49152, 106496, 229376, 491520, 1048576, 2228224, 4718592, 9961472, 20971520, 44040192, 92274688, 192937984, 402653184, 838860800, 1744830464, 3623878656, 7516192768, 15569256448, 32212254720
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Right side of the binomial sum Sum( (n-2*i)^2 * binomial(n, i), i=0..n) = n*2^n - Yong Kong (ykong(AT)curagen.com), Dec 28 2000
Let W be a binary relation on the power set P(A) of a set A having n = |A| elements such that for all elements x,y of P(A), xRy if x is a proper subset of y and there are no z in P(A) such that x is a proper subset of z and z is a proper subset of y, or y is a proper subset of x and there are no z in P(A) such that y is a proper subset of z and z is a proper subset of x. Then a(n) = |W|. - Ross La Haye (rlahaye(AT)new.rr.com), Sep 26 2007
Partial sums give A036799 -- Vladimir Joseph Stephan Orlovsky, Jul 09 2011.
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REFERENCES
| A. F. Horadam, Oresme numbers, Fib. Quart., 12 (1974), 267-271.
A. P. Prudnikov, Yu. A. Brychkov and O.I. Marichev, "Integrals and Series", Volume 1: "Elementary Functions", Chapter 4: "Finite Sums", New York, Gordon and Breach Science Publishers, 1986-1992, Eq. (4.2.2.29)
Ross La Haye, Binary Relations on the Power Set of an n-Element Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6. [From Ross La Haye (rlahaye(AT)new.rr.com), Feb 22 2009]
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..500
Index entries for sequences related to linear recurrences with constant coefficients, signature (4,-4).
C. Banderier and S. Schwer, Why Delannoy numbers?
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FORMULA
| Main diagonal of array (A085454) defined by T(i, 1)=i, T(1, j)=2j, T(i, j)=T(i-1, j)+T(i-1, j-1) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 05 2003
Binomial transform of A005843, the even numbers - Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Jan 13 2006
G.f.: 2x/(1-2x)^2 . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 21 2007
a(n) = A000079(n)*n. [From Omar E. Pol (info(AT)polprimos.com), Dec 21 2008]
E.g.f.: 2x exp(2x). - Geoffrey Critzer, Oct 03 2011
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MAPLE
| a:=n->sum(n*binomial(n+1, 2*j), j=0..n): seq(a(n), n=0..28); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 04 2007
g:=1/(1-2*z): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)*n, n=0..34); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 11 2009]
with(combinat):seq(n*numbcomb(n), n=0..28); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 17 2009]
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MATHEMATICA
| Table[n*2^n, {n, 0, 50}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 18 2010]
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PROG
| (PARI) a(n)=n<<n \\ Charles R Greathouse IV, Jun 15 2011
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CROSSREFS
| Equals 2*A001787. Equals A003261(n) + 1.
Cf. A000079, A036799, A096195, A097064.
Sequence in context: A131135 A097064 A134401 * A018045 A050242 A045697
Adjacent sequences: A036286 A036287 A036288 * A036290 A036291 A036292
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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