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A056545
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a(n) = 4*n*a(n-1) +1 with a(0)=1.
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5
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1, 5, 41, 493, 7889, 157781, 3786745, 106028861, 3392923553, 122145247909, 4885809916361, 214975636319885, 10318830543354481, 536579188254433013, 30048434542248248729, 1802906072534894923741, 115385988642233275119425
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| For positive n, a(n) equals 4^n times the permanent of the nXn matrix with (5/4)'s along the main diagonal and 1's everywhere else. [From John M. Campbell, Jul 10 2011]
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REFERENCES
| 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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FORMULA
| a(n) = floor( e^(1/4)*4^n*n! ).
a(n) = n!*sum(4^(n-k)/k!, k=0..n). E.g.f.: exp(x)/(1-4*x). - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Mar 14 2004
a(n) = Sum[P(n, k)*4^k, {k, 0, n}]. - Ross La Haye (rlahaye(AT)new.rr.com), Aug 29 2005
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EXAMPLE
| a(2)=4*2*a(1)+1=8*5+1=41
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CROSSREFS
| Cf. A000522, A010844, A010845, A056546, A056547 for analogues. A056545/(A000142*A000302) is an increasingly good approximation to 4th root of e.
Sequence in context: A049119 A032188 A143415 * A009755 A000685 A144286
Adjacent sequences: A056542 A056543 A056544 * A056546 A056547 A056548
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KEYWORD
| easy,nonn
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AUTHOR
| Henry Bottonley (se16(AT)btinternet.com), Jun 20 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 04 2000
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