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%I #29 Jul 14 2018 07:46:58
%S 1,2,10,92,1068,15352,265752,5368400,123919248,3217983008,92851377312,
%T 2947037232064,102040223376576,3827536020146048,154615082607931776,
%U 6691872388083371264,308938595472492867840,15153942107317778727424,787050616613300039649792
%N a(n) = Sum_{k>=1} H_n(k-1)/2^k, where H_n(x) is n-th Hermite polynomial.
%H G. C. Greubel, <a href="/A277380/b277380.txt">Table of n, a(n) for n = 0..380</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HermitePolynomial.html">Hermite Polynomial</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Hermite_polynomials">Hermite polynomials</a>
%F a(n) ~ c * 2^n * n! / (log(2))^n, where c = 0.639705404891769467944095575437073306645289161842121830191257596548619914238... - _Vaclav Kotesovec_, Jul 13 2018
%t Table[Sum[HermiteH[n, k - 1]/2^k, {k, 1, Infinity}], {n, 0, 20}]
%o (PARI) for(n=0,40, print1(if(n==0,1, ceil(sum(k=1, 15*n, polhermite(n, k-1)/2^k))), ", ")) \\ _G. C. Greubel_, Jul 13 2018
%o (PARI) nmax = 40; p = floor(2*log(nmax!*(2/log(2))^nmax)/log(10)); default(realprecision, p); a(n) = round(suminf(k=1, polhermite(n, k-1)/2^k));
%o for(n=0, nmax, print1(a(n), ", ")); \\ _Michel Marcus_ and _Vaclav Kotesovec_, Jul 13 2018
%Y Cf. A277381, A316778.
%K nonn
%O 0,2
%A _Vladimir Reshetnikov_, Oct 11 2016
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