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Search: id:A000354
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| A000354 |
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Expansion of e^{-x}/(1-2*x).
(Formerly M3957 N1631)
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+0
10
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| 1, 1, 5, 29, 233, 2329, 27949, 391285, 6260561, 112690097, 2253801941, 49583642701, 1190007424825, 30940193045449, 866325405272573, 25989762158177189, 831672389061670049, 28276861228096781665, 1017967004211484139941
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) is the permanent of the n X n matrix with 1 on the diagonal and 2 elsewhere. - Yuval Dekel, Nov 01 2003
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 83.
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.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
E. Lucas, Th\'{e}orie des Nombres. Gauthier-Villars, Paris, 1891, Vol. 1, p. 223.
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FORMULA
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Inverse binomial transform of double factorials A000165 - Paul Barry (pbarry(AT)wit.ie), May 26 2003
a(n)=sum{k=0..n, (-1)^(n+k)C(n, k)k!2^k } - Paul Barry (pbarry(AT)wit.ie), May 26 2003
a(n)= Sum(k=0..n, A008290(n, k)*2^(n-k)) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 13 2003
a(n)=2n*a(n-1)+(-1)^n, n>0, a(0)=1. - Paul Barry (pbarry(AT)wit.ie), Aug 26 2004
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MAPLE
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BB := (x, k)->k!*sum(sum(x^j/((k-j)!^2*j!), j=1..k), m=1..k): R := (x, n, k)->BB(x, k)^n: f := (t, n, k)->sum(coeff(R(x, n, k), x, j)*(t-1)^j*(n*k-j)!, j=0..n*k): > seq(abs(f(0, n, 2)/2!^n), n=0..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 26 2007
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MATHEMATICA
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Table[ Gamma[ n, -1/2 ]*2^(n-1)/Exp[ 1/2 ], {n, 1, 24} ]; FunctionExpand[ % ]
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CROSSREFS
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Cf. A061714.
Cf. A008290.
Adjacent sequences: A000351 A000352 A000353 this_sequence A000355 A000356 A000357
Sequence in context: A057623 A087662 A113012 this_sequence A103815 A134752 A112799
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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