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A002114 Glaisher's H' numbers.
(Formerly M4810 N2057)
+0
5
1, 11, 301, 15371, 1261501, 151846331, 25201039501, 5515342166891, 1538993024478301, 533289474412481051, 224671379367784281901, 113091403397683832932811, 67032545884354589043714301, 46211522130188693681603906171 (list; graph; listen)
OFFSET

1,2

COMMENT

(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]

REFERENCES

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.

LINKS

Index entries for sequences related to Glaisher's numbers

FORMULA

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

CROSSREFS

Sequence in context: A101269 A012184 A012027 this_sequence A012192 A012079 A001280

Adjacent sequences: A002111 A002112 A002113 this_sequence A002115 A002116 A002117

KEYWORD

nice,easy,nonn

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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Last modified December 17 19:39 EST 2009. Contains 170821 sequences.


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