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

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..380

Eric Weisstein's World of Mathematics, Hermite Polynomial

Wikipedia, Hermite polynomials

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

Mathematica

Table[Sum[HermiteH[n, k - 1]/2^k, {k, 1, Infinity}], {n, 0, 20}]

Prog

(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
(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

Crossrefs

Cf. A277381, A316778.

Sequence in context: A086587 A082472 A095937 * A108528 A181136 A182952

Adjacent sequences: A277377 A277378 A277379 * A277381 A277382 A277383

Keyword

nonn

Author

Vladimir Reshetnikov, Oct 11 2016

Status

approved