0,2

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

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]

T. D. Noe, Table of n, a(n) for n=0..500

Index entries for sequences related to linear recurrences with constant coefficients

C. Banderier and S. Schwer, Why Delannoy numbers?

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]

(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

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

with(finance):seq(add(futurevalue( 2, 1, n), k=0..n), n=-1..27); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 20 2008

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]

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]

Equals 2*A001787. Equals A003261(n) + 1.

Cf. A096195, A097064.

Cf. A000079. [From Omar E. Pol (info(AT)polprimos.com), Dec 21 2008]

Sequence in context: A006730 A131135 A134401 this_sequence A097064 A018045 A050242

Adjacent sequences: A036286 A036287 A036288 this_sequence A036290 A036291 A036292

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).