cp's OEIS Frontend

A139756 Binomial transform of A004526.

%I A139756 #29 May 06 2024 12:10:25
%S A139756 0,0,1,4,12,32,80,192,448,1024,2304,5120,11264,24576,53248,114688,
%T A139756 245760,524288,1114112,2359296,4980736,10485760,22020096,46137344,
%U A139756 96468992,201326592,419430400,872415232,1811939328,3758096384,7784628224,16106127360,33285996544
%N A139756 Binomial transform of A004526.
%C A139756 Essentially the same as A001787, A097067, A085750 and A118442.
%C A139756 Also: self-convolution of A131577. - _R. J. Mathar_, May 22 2008
%C A139756 Let S be a subset of {1,2,...,n}.  A succession in S is a subset of the form {i,i+1}.  a(n) is the total number of successions in all subsets of {1,2,...,n}.  a(n) = Sum_{k>=1} A076791(n,k)*k. - _Geoffrey Critzer_, Mar 18 2012.
%D A139756 I Goulden and D Jackson, Combinatorial Enumeration, John Wiley and Sons, 1983, page 55.
%H A139756 Vincenzo Librandi, <a href="/A139756/b139756.txt">Table of n, a(n) for n = 0..1000</a>
%H A139756 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).
%F A139756 O.g.f.: x^2/(1-2*x)^2. a(n) = (n-1)*2^n/4 if n>0. - _R. J. Mathar_, May 22 2008
%F A139756 a(n) = A097067(n), n>0. - _R. J. Mathar_, Nov 03 2008
%F A139756 a(n) = A168511(n+1,n). - _Philippe Deléham_, Mar 20 2013
%F A139756 a(n) = 2*a(n-1) + 2^(n-2), n>=2. - _Philippe Deléham_, Mar 20 2013
%e A139756 a(4) = 12 because we have {1,2}, {2,3}, {3,4}, {1,2,4}, {1,3,4} with one succession; {1,2,3}, {2,3,4} with two successions; and {1,2,3,4} with three successions. - _Geoffrey Critzer_, Mar 18 2012.
%t A139756 nn = 30; a = 1/(1 - y x); b = x/(1 - y x) + 1; c = 1/(1 - x); CoefficientList[ D[Series[c b/(1 - (a x^2 c)), {x, 0, nn}], y] /. y -> 1, x]  (* _Geoffrey Critzer_, Mar 18 2012 *)
%Y A139756 Cf. A001787, A004526, A076791, A085750, A097067, A118442, A131577, A168511.
%K A139756 nonn,easy
%O A139756 0,4
%A A139756 _Paul Curtz_, May 19 2008
%E A139756 More terms from _R. J. Mathar_, May 22 2008