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A122704
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a(n)=Sum_{k, 0<=k<=n}3^(n-k)*A123125(n,k).
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4
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1, 1, 4, 22, 160, 1456, 15904, 202672, 2951680, 48361216, 880405504, 17630351872, 385148108800, 9114999832576, 232311251144704, 6343764407375872, 184778982658539520
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n+1)=[1,4,22,160,1456,...]is the first Eulerian transform of A000244 (powers of 3), it is also the Stirling transform of A080599(n+1)=[1,3,12,66,450,...].
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FORMULA
| O.g.f.: Sum_{n>=0} n! * x^n / Product_{k=1..n} (1-2*k*x). [From Paul D. Hanna, Jul 20 2011]
a(n) = Sum_{k, 0<=k<=n} A131689(n,k)*2^(n-k). - Philippe DELEHAM, Oct 09 2007
a(n) = A_{n}(3) where A_{n}(x) are the <a href="http://oeis.org/wiki/Eulerian_polynomials"> Eulerian polynomials</a>. - Peter Luschny
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PROG
| (PARI) {a(n)=polcoeff(sum(m=0, n, m!*x^m/prod(k=1, m, 1-2*k*x+x*O(x^n))), n)} /* Paul D. Hanna, Jul 20 2011 */
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CROSSREFS
| Sequence in context: A112697 A113717 A124563 * A087547 A184942 A000779
Adjacent sequences: A122701 A122702 A122703 * A122705 A122706 A122707
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KEYWORD
| nonn
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 22 2006
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EXTENSIONS
| a(7) corrected (was 206672), a(n) extended, formula added Peter Luschny (peter(AT)luschny.de), Aug 03 2010
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