%I A002114 M4810 N2057
%S A002114 1,11,301,15371,1261501,151846331,25201039501,5515342166891,1538993024478301,
%T A002114 533289474412481051,224671379367784281901,113091403397683832932811,
%U A002114 67032545884354589043714301,46211522130188693681603906171
%N A002114 Glaisher's H' numbers.
%C A002114 (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]
%D A002114 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002114 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002114 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.
%D A002114 J. W. L. Glaisher, On a set of coefficients analogous to the Eulerian 
               numbers, Proc. London Math. Soc., 31 (1899), 216-235.
%H A002114 <a href="Sindx_Ge.html#Glaisher">Index entries for sequences related 
               to Glaisher's numbers</a>
%F A002114 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).
%F A002114 H'(n) = A000436(n)/2^(2n+1) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), 
               Jan 17 2004
%F A002114 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
%Y A002114 Sequence in context: A101269 A012184 A012027 this_sequence A012192 A012079 
               A001280
%Y A002114 Adjacent sequences: A002111 A002112 A002113 this_sequence A002115 A002116 
               A002117
%K A002114 nice,easy,nonn
%O A002114 1,2
%A A002114 N. J. A. Sloane (njas(AT)research.att.com).