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A005799
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Generalized Euler numbers of type 2^n.
(Formerly M1979)
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3
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1, 1, 2, 10, 104, 1816, 47312, 1714000, 82285184, 5052370816, 386051862272, 35917232669440, 3996998043812864, 524203898507631616, 80011968856686405632, 14061403972845412526080, 2818858067801804443910144
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| This is the BinomialMean transform of A000364 (see A075271 for definition of transform). - John W. Layman (layman(AT)math.vt.edu), Dec 04 2002
This sequence appears to be middle column in Poupard's triangle A008301.
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REFERENCES
| Gessel, Ira M.; Symmetric functions and P-recursiveness. J. Combin. Theory Ser. A 53 (1990), no. 2, 257-285.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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) = 1/2^n * sum_{i=0..n} binomial(n, i) * A000364(i).
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MATHEMATICA
| a[n_] := Sum[Binomial[n, i]Abs[EulerE[2i]], {i, 0, n}]/2^n
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CROSSREFS
| Sequence in context: A086927 A135058 A154256 * A000595 A087234 A049538
Adjacent sequences: A005796 A005797 A005798 * A005800 A005801 A005802
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 10 2002
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