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A079492 Nearest integer to Sum_{k=0..n} binomial(n,k)/2^(k*(k-1)/2).

%I A079492 #8 Sep 08 2022 08:45:08
%S A079492 1,2,4,6,9,12,17,23,31,41,52,66,82,101,124,150,180,215,254,299,351,
%T A079492 408,473,546,628,719,820,932,1055,1192,1342,1508,1689,1887,2104,2340,
%U A079492 2597,2876,3179,3507,3863,4247,4662,5108,5590,6107,6663,7259,7899,8583,9316,10099
%N A079492 Nearest integer to Sum_{k=0..n} binomial(n,k)/2^(k*(k-1)/2).
%D A079492 D. L. Kreher and D. R. Stinson, Combinatorial Algorithms, CRC Press, 1999, p. 113.
%H A079492 G. C. Greubel, <a href="/A079492/b079492.txt">Table of n, a(n) for n = 0..1000</a>
%e A079492 1, 2, 7/2, 45/8, 545/64, 12625/1024, 564929/32768, 49162689/2097152, ...
%p A079492 f := n->add(binomial(n,k)/2^(k*(k-1)/2),k=0..n);
%t A079492 Table[Round[Sum[Binomial[n,k]/2^(k*(k-1)/2), {k,0,n}]], {n,0,60}] (* _G. C. Greubel_, Jan 18 2019 *)
%o A079492 (PARI) vector(60, n, n--; round(sum(k=0,n, binomial(n,k)/2^(k*(k-1)/2)))) \\ _G. C. Greubel_, Jan 18 2019
%o A079492 (Magma) [Round( (&+[Binomial(n,k)/2^(k*(k-1)/2): k in [0..n]]) ): n in [0..60]]; // _G. C. Greubel_, Jan 18 2019
%o A079492 (Sage) [round(sum(binomial(n,k)/2^(k*(k-1)/2) for k in (0..30))) for n in (0..60)] # _G. C. Greubel_, Jan 18 2019
%Y A079492 Cf. A079491.
%K A079492 nonn
%O A079492 0,2
%A A079492 _N. J. A. Sloane_, Jan 20 2003