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Search: id:A002114
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| A002114 |
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Glaisher's H' numbers. (Formerly M4810 N2057)
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+0 5
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| 1, 11, 301, 15371, 1261501, 151846331, 25201039501, 5515342166891, 1538993024478301, 533289474412481051, 224671379367784281901, 113091403397683832932811, 67032545884354589043714301, 46211522130188693681603906171
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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(a(n)=A002114) mod 9 = period 6:repeat 1,2,4,8,7,5 =A153130; (see also A001370). Hence 0, 9, 297, 15363, 1261494, 151846326, . Last digit is 1's=A000012.Hence multiples of 10. Consider a(n) by ten terms last (2?) digits: 1,11,(3)01,71,01,31,01,91,01,51, 1,11,(3)01,71, . [From Paul Curtz (bpcrtz(AT)free.fr), Sep 10 2009]
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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).
A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 76.
J. W. L. Glaisher, On a set of coefficients analogous to the Eulerian numbers, Proc. London Math. Soc., 31 (1899), 216-235.
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LINKS
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Index entries for sequences related to Glaisher's numbers
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FORMULA
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H'(n) = H(n)/3, where H(n)=2^(2n+1)*I(n) (see A002112) and e.g.f. for (-1)^n*I(n) is (3/2)/(1+exp(x)+exp(-x)) (see A047788, A047789).
H'(n) = A000436(n)/2^(2n+1) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 17 2004
For n > 0, H'(n) = Sum{k = 0..n, T(n, k)*9^(n-k)*2^(k-1) }; where DELTA is the operator defined in A084938, T(n, k) is the triangle, read by rows, given by :[0, 1, 0, 4, 0, 9, 0, 16, 0, 25, ...] DELTA [1, 0, 10, 0, 28, 0, 55, 0, 90, ..]= {1}; {0, 1}; {0, 1, 1}; {0, 1, 12, 1}; {0, 1, 63, 123, 1}; {0, 1, 274, 2366, 1234, 1}; ... For 1, 10, 28, 55, 90, 136, ... see A060544 or A060544 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 17 2004
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CROSSREFS
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Sequence in context: A101269 A012184 A012027 this_sequence A012192 A012079 A001280
Adjacent sequences: A002111 A002112 A002113 this_sequence A002115 A002116 A002117
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KEYWORD
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nice,easy,nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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