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.

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