A277380 a(n) = Sum_{k>=1} H_n(k-1)/2^k, where H_n(x) is n-th Hermite polynomial.
1, 2, 10, 92, 1068, 15352, 265752, 5368400, 123919248, 3217983008, 92851377312, 2947037232064, 102040223376576, 3827536020146048, 154615082607931776, 6691872388083371264, 308938595472492867840, 15153942107317778727424, 787050616613300039649792
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..380
- Eric Weisstein's World of Mathematics, Hermite Polynomial
- Wikipedia, Hermite polynomials
Programs
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Mathematica
Table[Sum[HermiteH[n, k - 1]/2^k, {k, 1, Infinity}], {n, 0, 20}] -
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
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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)); for(n=0, nmax, print1(a(n), ", ")); \\ Michel Marcus and Vaclav Kotesovec, Jul 13 2018
Formula
a(n) ~ c * 2^n * n! / (log(2))^n, where c = 1/(2 * log(2) * exp(log(2)^2/4)) = 0.639705404891769467944095575437073306645289161842121830191257596548619914238... - Vaclav Kotesovec, Jul 13 2018, updated Apr 21 2024