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A002999
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Expansion of (1+x*exp(x))^2.
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3
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1, 2, 6, 18, 56, 170, 492, 1358, 3600, 9234, 23060, 56342, 135192, 319514, 745500, 1720350, 3932192, 8912930, 20054052, 44826662, 99614760, 220201002, 484442156, 1061158958, 2315255856, 5033164850, 10905190452, 23555211318, 50734301240, 108984795194
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| T. D. Noe, Table of n, a(n) for n = 0..500
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FORMULA
| a(0) = 1, a(n) = (n^2-n)2^n/4 + 2n. a(n) = A003013(n) + n = A001815(n) + 2n. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 02 2003
G.f.: 1+(2x(7x^3-10x^2+5x-1))/((x-1)^2 (2x-1)^3) [From Harvey P. Dale, Apr 04 2011]
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MATHEMATICA
| CoefficientList[Series[1+(2x(7x^3-10x^2+5x-1))/((x-1)^2 (2x-1)^3), {x, 0, 30}], x] (* From Harvey P. Dale, Apr 04 2011 *)
Table[If[n == 0, 1, (n^2 - n) 2^n/4 + 2*n], {n, 0, 30}] (* T. D. Noe, Apr 04 2011 *)
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CROSSREFS
| Cf. A048482, A001787, A005183.
Sequence in context: A148456 A148457 A182881 * A091142 A111961 A190861
Adjacent sequences: A002996 A002997 A002998 * A003000 A003001 A003002
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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