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Search: id:A000994
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| A000994 |
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Shifts 2 places left under binomial transform.
(Formerly M1446 N0572)
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+0
8
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| 1, 0, 1, 1, 2, 5, 13, 36, 109, 359, 1266, 4731, 18657, 77464, 337681, 1540381, 7330418, 36301105, 186688845, 995293580, 5491595645, 31310124067, 184199228226, 1116717966103, 6968515690273, 44710457783760, 294655920067105
(list; graph; listen)
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OFFSET
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0,5
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
S. Tauber, On generalizations of the exponential function, Amer. Math. Monthly, 67 (1960), 763-767.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210.
N. J. A. Sloane, Transforms
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FORMULA
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Since this satisfies a recurrence similar to that of the Bell numbers (A000110), the asymptotic behavior is presumably just as complicated - see A000110 for details.
However, A000994(n)/A000995(n) [ e.g. 77464/63117 ] -> 1.228..., the constant in A051148 and A051149.
O.g.f.: A(x) = Sum_{n>=0} x^(2*n)*(1-n*x)/Product_{k=0..n} (1-k*x)^2 . - Paul D. Hanna (pauldhanna(AT)juno.com), Nov 02 2006
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EXAMPLE
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A(x) = 1 + x^2/(1-x) + x^4/((1-x)^2*(1-2x)) + x^6/((1-x)^2*(1-2x)^2*(1-3x)) +...
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MAPLE
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A000994 := proc(n) local k; option remember; if n <= 1 then 1 else 1 + add(binomial(n, k)*A000994(k - 2), k = 2 .. n); fi; end;
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PROGRAM
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(PARI) a(n)=polcoeff(sum(k=0, n, x^(2*k)*(1-k*x)/prod(j=0, k, 1-j*x+x*O(x^n))^2), n) - Paul D. Hanna (pauldhanna(AT)juno.com), Nov 02 2006
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CROSSREFS
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Cf. A000995, A051139, A051140.
Sequence in context: A133365 A135335 A066723 this_sequence A148296 A148297 A148298
Adjacent sequences: A000991 A000992 A000993 this_sequence A000995 A000996 A000997
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KEYWORD
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nonn,easy,nice,eigen
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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