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A007466
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Exponential-convolution of natural numbers with themselves.
(Formerly M3478)
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2
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1, 4, 14, 44, 128, 352, 928, 2368, 5888, 14336, 34304, 80896, 188416, 434176, 991232, 2244608, 5046272, 11272192, 25034752, 55312384, 121634816, 266338304, 580911104, 1262485504, 2734686208, 5905580032, 12717129728
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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
| E.g.f.: (Sum_{n >= 1} n*x^(n-1)/(n-1)!)^2.
a(n) = Sum_{k=0..(n+2)} C(n+2, k) * floor(k/2)^2 - Paul Barry, Mar 06 2003
E.g.f.: (1+x)^2*exp(2*x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 09 2003
G.f.: -(2*x^3-2*x^2+x)/(8*x^3-12*x^2+6*x-1). - Vladimir Kruchinin, Sep 28 2011
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MAPLE
| n->2^n*(n+1)+1/4*2^n*n*(n-1);
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CROSSREFS
| Sequence in context: A084613 A099063 A057223 * A062109 A118042 A006645
Adjacent sequences: A007463 A007464 A007465 * A007467 A007468 A007469
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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