%I A036289
%S A036289 0,2,8,24,64,160,384,896,2048,4608,10240,22528,49152,106496,229376,
%T A036289 491520,1048576,2228224,4718592,9961472,20971520,44040192,92274688,
%U A036289 192937984,402653184,838860800,1744830464,3623878656,7516192768
%N A036289 n*2^n.
%C A036289 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
%C A036289 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
%D A036289 A. F. Horadam, Oresme numbers, Fib. Quart., 12 (1974), 267-271.
%D A036289 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)
%D A036289 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]
%H A036289 T. D. Noe, <a href="b036289.txt">Table of n, a(n) for n=0..500</a>
%H A036289 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to
linear recurrences with constant coefficients</a>
%H A036289 C. Banderier and S. Schwer, <a href="http://arXiv.org/abs/math.CO/0411128">
Why Delannoy numbers?</a>
%F A036289 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
%F A036289 Binomial transform of A005843, the even numbers - Joshua Zucker (joshua.zucker(AT)stanfordalumni.org),
Jan 13 2006
%F A036289 G.f.: 2x/(1-2x)^2 . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov
21 2007
%F A036289 a(n) = A000079(n)*n. [From Omar E. Pol (info(AT)polprimos.com), Dec 21
2008]
%p A036289 (1+1); ((2+2)+(2+2)); (((3+3)+(3+3))+((3+3)+(3+3))); ((((4+4)+(4+4))+((4+4)+(4+4)))+(((4+4)+(4+4))+((4+4)+(4+\
4)))); (((((5+5)+(5+5))+((5+5)+(5+5)))+(((5+5)+(5+5))+((5+5)+(5+5))))+((((5+5)+(5+5))+((5+5)+(5+5)))+(((5\
+5)+(5+5))+((5+5)+(5+5))))); ((((((6+6)+(6+6))+((6+6)+(6+6)))+(((6+6)+(6+6))+((6+6)+(6+6))))+((((6+6)+(6+\
6))+((6+6)+(6+6)))+(((6+6)+(6+6))+((6+6)+(6+6)))))+(((((6+6)+(6+6))+((6+6)+(6+6)))+(((6+6)+(6+6))+((6+6)+\
(6+6))))+((((6+6)+(6+6))+((6+6)+(6+6)))+(((6+6)+(6+6))+((6+6)+(6+6))))));
- Jorge Coveiro (jorgecoveiro(AT)yahoo.com), Dec 26 2004
%p A036289 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
%p A036289 with(finance):seq(add(futurevalue( 2, 1, n),k=0..n),n=-1..27); - Zerinvary
Lajos (zerinvarylajos(AT)yahoo.com), Jun 20 2008
%p A036289 a:=n->sum (2^n, j=0..n-1): seq(a(n), n=0..30);# [From Zerinvary Lajos
(zerinvarylajos(AT)yahoo.com), Dec 17 2008]
%p A036289 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]
%p A036289 with(combinat):seq(n*numbcomb(n), n=0..28);# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com),
Apr 17 2009]
%Y A036289 Equals 2*A001787. Equals A003261(n) + 1.
%Y A036289 Cf. A096195, A097064.
%Y A036289 Cf. A000079. [From Omar E. Pol (info(AT)polprimos.com), Dec 21 2008]
%Y A036289 Sequence in context: A006730 A131135 A134401 this_sequence A097064 A018045
A050242
%Y A036289 Adjacent sequences: A036286 A036287 A036288 this_sequence A036290 A036291
A036292
%K A036289 nonn,easy,nice
%O A036289 0,2
%A A036289 N. J. A. Sloane (njas(AT)research.att.com).
|
