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A020543
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a(0) = 1, a(1) = 1, a(n+1) = (n+1)*a(n)+n.
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1
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1, 1, 3, 11, 47, 239, 1439, 10079, 80639, 725759, 7257599, 79833599, 958003199, 12454041599, 174356582399, 2615348735999, 41845579775999, 711374856191999, 12804747411455999, 243290200817663999, 4865804016353279999
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| First Bernoulli polynomial evaluated at x=n! (multiplied by 2).
a(0) = 1, for n >= 1: a(n) = numbers m for which there is one iteration {floor (r / k)} for k = n, n-1, n-2, ... 1 with property r mod k = k-1 starting at r = m. For n = 5: a(5) = 239; floor (239 / 5) = 47, 239 mod 5 = 4; floor (47 / 4) = 11, 47 mod 4 = 3; floor (11 / 3) = 3, 11 mod 3 = 2; floor (3 / 2) = 1; 3 mod 2 = 1; floor (1 / 1) = 1, 1 mod 1 = 0. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Jan 23 2010]
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LINKS
| Index entries for sequences related to Bernoulli numbers.
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FORMULA
| E.g.f.: (-2+exp(x)-x*exp(x))/(1-x). - Ralf Stephan, Feb 18 2004
a(n) = 2*n! - 1 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 07 2008
a(0) = a(1) = 1, a(n) = a(n-1) * n + (n-1) for n >= 2. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Jan 23 2010]
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MATHEMATICA
| lst={1}; s=1; Do[s+=(n+=s*n); AppendTo[lst, s], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 10 2008]
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CROSSREFS
| A052898(n) - 2.
Sequence in context: A030865 A030902 A030925 * A111139 A167564 A191344
Adjacent sequences: A020540 A020541 A020542 * A020544 A020545 A020546
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KEYWORD
| nonn
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AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| Better description from Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 29 2001
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