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%I #29 Nov 16 2017 02:38:58
%S 1,2,6,34,422,11586,678982,82653026,20565923814,10362872458882,
%T 10517568142605446,21434335059927667362,87558678536857464017446,
%U 716228573446369122069676994,11725371140175829761708518252742
%N BinomialMean (BM) transform of A075271, which see for the definition of (BM).
%C a(n) = 2*A075271(n-1), for n >= 1.
%C Binomial transform of A005329. - _Vladimir Reshetnikov_, Nov 20 2015
%H Alois P. Heinz, <a href="/A075272/b075272.txt">Table of n, a(n) for n = 0..50</a>
%H Michael Z. Spivey and Laura L. Steil, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Spivey/spivey7.html"> The k-Binomial Transforms and the Hankel Transform</a>, J. Integ. Seqs. Vol. 9 (2006), #06.1.1.
%F G.f.: Sum_{n>=0} x^n*Product_{i=1..n}(2^i/(1+(2^i-1)*x)). - _Vladeta Jovovic_, Mar 10 2008
%F O.g.f. as a continued fraction of Stieltjes's type: 1/(1 - 2*x/(1 - x/(1 - 2^3*x/(1 - 3^2*x/(1 - 2^5*x/(1 - 7^2*x/(1 - 2^7*x/(1 - 15^2*x/(1 - 2^9*x/(1 - 31^2*x - ... )))))))))). Cf. A005329. - _Peter Bala_, Nov 10 2017
%p iBM:= proc(p) proc (n) option remember; add (2^(k) *p(k) *(-1)^(n-k) *binomial(n,k), k=0..n) end end: a:='a': aa:= iBM(a): a:= n-> `if` (n=0, 1, 2*aa(n-1)): seq (a(n), n=0..16); # _Alois P. Heinz_, Sep 09 2008
%t Table[Sum[QFactorial[k, 2] Binomial[n, k], {k, 0, n}], {n, 0, 15}] (* _Vladimir Reshetnikov_, Oct 16 2016 *)
%Y Cf. A075271, A005329.
%K nonn,easy
%O 0,2
%A _John W. Layman_, Sep 11 2002
%E More terms from _Alois P. Heinz_, Sep 09 2008
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