Search: id:A005494
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%I A005494 M3540
%S A005494 1,4,17,77,372,1915,10481,60814,372939,2409837,16360786,116393205,
%T A005494 865549453,6713065156,54190360453,454442481041,3952241526188,35590085232519,
%U A005494 331362825860749,3185554606447814,31581598272055879,322516283206446897
%N A005494 E.g.f.: exp(3*z+exp(z)-1).
%C A005494 From expansion of falling factorials (binomial transform of A005493).
%D A005494 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005494 E. G. Whitehead, Jr., Stirling number identities from chromatic polynomials, 
               J. Combin. Theory, A 24 (1978), 314-317.
%H A005494 J. W. Layman, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               The Hankel Transform and Some of its Properties</a>, J. Integer Sequences, 
               4 (2001), #01.1.5.
%H A005494 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%F A005494 a(n) = Sum_{i=0..n} 3^(n-i)*B(i)*binomial(n,i) where B(n) = Bell numbers 
               A000110(n). - Fred Lunnon, Aug 04 2007
%F A005494 a(n) = exp(-1)*sum(k=>0, (k+3)^(n)/k!) - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), 
               Jun 03 2004. May be rewritten as a(n)=sum(k^n*(k-1)*(k-2)/k!,k=3..infinity)/
               exp(1), which is a Dobinski-type relation for this sequence. - Karol 
               A. Penson (penson(AT)lptl.jussieu.fr), Aug 18 2006
%F A005494 Define f_1(x),f_2(x),... such that f_1(x)=x^2*e^x, f_{n+1}(x)=diff(x*f_n(x),
               x), for n=2,3,.... Then a(n-1)=e^{-1}*f_n(1). - Milan R. Janjic (agnus(AT)blic.net), 
               May 30 2008
%Y A005494 Cf. A000110, A005493.
%Y A005494 Sequence in context: A151248 A104455 A123952 this_sequence A053486 A151249 
               A110307
%Y A005494 Adjacent sequences: A005491 A005492 A005493 this_sequence A005495 A005496 
               A005497
%K A005494 nonn
%O A005494 0,2
%A A005494 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)

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