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A045379
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E.g.f.: exp(4*z+exp(z)-1).
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5
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1, 5, 26, 141, 799, 4736, 29371, 190497, 1291020, 9131275, 67310847, 516369838, 4116416797, 34051164985, 291871399682, 2588914083065, 23733360653955, 224592570163192, 2191466128865567, 22024934452712437, 227771488390279260
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| J. W. Layman, The Hankel Transform and Some of its Properties, J. Integer Sequences, 4 (2001), #01.1.5.
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FORMULA
| a(n) = EXP(-1)*sum(k=>0, (k+4)^(n)/k!) - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Jun 03 2004
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
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
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EXAMPLE
| Let A be the upper Hessenberg matrix of order n defined by: A[i,i-1]=-1, A[i,j]=binomial(j-1,i-1), (i<=j), and A[i,j]=0 otherwise. Then, for n>=1, a(n)=(-1)^(n)charpoly(A,-4). [From Milan R. Janjic (agnus(AT)blic.net), Jul 08 2010]
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CROSSREFS
| Cf. A000110 A005493 A005494.
Cf. A000110, A005493, A005494, A045379.
Equals the row sums of triangle A143496. [From Wolfdieter Lang, Sep 29 2011]
Sequence in context: A081911 A081187 A104498 * A053487 A183161 A082029
Adjacent sequences: A045376 A045377 A045378 * A045380 A045381 A045382
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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