0,2

Incomplete Gamma Function at 2.

Let P(A) be the power set of an n-element set A. Then a(n) = the total number of ways to add 0 or more elements of A to each element x of P(A) where the elements to add are not elements of x and order of addition is important. - Ross La Haye (rlahaye(AT)new.rr.com), Nov 19 2007

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 262.

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.1.2.

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..100

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 262.

J. W. Layman, The Hankel Transform and Some of its Properties, J. Integer Sequences, 4 (2001), #01.1.5.

a(n) = row sums of A090802. - Ross La Haye (rlahaye(AT)new.rr.com), Aug 18 2006

a(n) = n*a(n-1)+2^n = (n+2)a(n-1)-(2n-2)a(n-2) = n!*sum{0 <= j <= n}[ 2^j/j! ] - Henry Bottomley (se16(AT)btinternet.com), Jul 12 2001

a(n) is the permanent of the n X n matrix with 3's on the diagonal and 1's elsewhere. a(n) = Sum(k=0..n, A008290(n, k)*3^k). - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 12 2003

Binomial transform of A000522. - Ross La Haye (rlahaye(AT)new.rr.com), Sep 15 2004

a(n)=sum{k=0..n, k!*C(n, k)2^(n-k)}; - Paul Barry (pbarry(AT)wit.ie), Apr 22 2005

a(n) = A066534(n) + 2^n. - Ross La Haye (rlahaye(AT)new.rr.com), Nov 16 2005

a(n) is the number of ways to split the set {1,2,...,n} into two disjoint subsets S,T with S union T = {1,2,...,n} and linearly order S and then choose a subset of T. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Mar 10 2009]

restart: G(x):=exp(2*x)/(1-x): f[0]:=G(x): for n from 1 to 19 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..19); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 03 2009]

Table[ Gamma[ n, 2 ]*E^2, {n, 1, 24} ]

Cf. A053484, A053485, A053486, A008290.

A010843, A000023, A000166, A000142, A000522, A010842, A053486, A053487 have similar properties.

Sequence in context: A151063 A103138 A074527 this_sequence A140710 A103296 A111749

Adjacent sequences: A010839 A010840 A010841 this_sequence A010843 A010844 A010845

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)