0,2

Related to Incomplete Gamma Function at 1/2.

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

Mathieu Guay-Paquet and Jeffrey Shallit, Avoiding Squares and Overlaps Over the Natural Numbers (2009) http://arxiv.org/abs/0901.1397. Discrete Math., 309 (2009), 6245-6254. [From N. J. A. Sloane, Nov 27 2009]

Michael Z. Spivey and Laura L. Steil, The k-Binomial Transforms and the Hankel Transform, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.

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.

[ e^(1/2)n!2^n ]; n!*Sum(2^(n-k)/k!, k=0..n) (i.e. binomial transform of (2n)!!=n!2^n); n!*(e^(1/2)-Sum(2^(n-k)/k!, k=n+1...)).

a(n) = A056541(n)+A000165(n). - Henry Bottomley (se16(AT)btinternet.com), Jun 20 2000

E.g.f.: exp(x)/(1-2*x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 11 2002

Sum_{n >= 1} 1/a(n) = 0.4246665348160769533082551230... - Cino Hilliard (hillcino368(AT)gmail.com), Aug 19 2003

a(n) = Sum[P(n, k)2^k, {k, 0, n}]. - Ross La Haye (rlahaye(AT)new.rr.com), Aug 29 2005

a(3)=2*3*a(2)+1=6*13+1=79

Table[ Gamma[ n, 1/2 ]*Exp[ 1/2 ]*2^(n-1), {n, 1, 24} ]

...and/or... s=1; lst={}; Do[s+=s++n; AppendTo[lst, s], {n, 1, 5!, 2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 23 2008]

Cf. A000522, A010845, A007566, A000165.

Sequence in context: A062872 A159312 A125659 this_sequence A090364 A112935 A074514

Adjacent sequences: A010841 A010842 A010843 this_sequence A010845 A010846 A010847

easy,nonn

Simon Plouffe (simon.plouffe(AT)gmail.com)

Better description and formulae from Michael Somos