%I A045379
%S A045379 1,5,26,141,799,4736,29371,190497,1291020,9131275,67310847,516369838,
%T A045379 4116416797,34051164985,291871399682,2588914083065,23733360653955,
%U A045379 224592570163192,2191466128865567,22024934452712437,227771488390279260
%N A045379 E.g.f.: exp(4*z+exp(z)-1).
%H A045379 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.
%F A045379 a(n) = EXP(-1)*sum(k=>0, (k+4)^(n)/k!) - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), 
               Jun 03 2004
%F A045379 A recursive formula to compute some integer sequences (including A000110, 
               A005493, A005494 and the present sequence). Define G(n, m), where 
               n, m >= 0, as follows: G(0, m) = 1; G(n, m) = G(n-1, m) * (m+1) + 
               G(n-1, m+1), where n > 0. Then G(n, 0) = A000110(n+1); G(n, 1) = 
               A005493(n+1); G(n, 2) = A005494(n+1); G(n, 3) = A045379(n+1) - Alexey 
               Andreev (ava12(AT)nm.ru), Jan 05 2006
%F A045379 Define f_1(x),f_2(x),... such that f_1(x)=x^3*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 A045379 Cf. A000110 A005493 A005494.
%Y A045379 Cf. A000110, A005493, A005494, A045379.
%Y A045379 Sequence in context: A081911 A081187 A104498 this_sequence A053487 A082029 
               A001705
%Y A045379 Adjacent sequences: A045376 A045377 A045378 this_sequence A045380 A045381 
               A045382
%K A045379 nonn
%O A045379 0,2
%A A045379 N. J. A. Sloane (njas(AT)research.att.com).