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A316778 a(n) = exp(-1/2) * Sum_{k>=0} H_n(k) / (k!*2^k), where H_n(x) is n-th Hermite polynomial. 3
1, 1, 1, 5, 25, 97, 489, 3285, 22481, 160737, 1293041, 11348933, 105136937, 1033279873, 10808289561, 119401994709, 1385242479137, 16846680046657, 214333419288161, 2844927602028549, 39305588104667321, 564208058072724257, 8400178767847987401, 129509650839484638037 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..500

FORMULA

E.g.f.: exp(exp(2*x)/2 - x^2 - 1/2).

MATHEMATICA

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

nmax = 20; CoefficientList[Series[Exp[Exp[2*x]/2 - x^2 - 1/2], {x, 0, nmax}], x] * Range[0, nmax]!

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

CROSSREFS

Cf. A277380, A277381.

Sequence in context: A273747 A201841 A146830 * A255612 A022729 A098111

Adjacent sequences:  A316775 A316776 A316777 * A316779 A316780 A316781

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jul 13 2018

STATUS

approved

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Last modified March 22 17:25 EDT 2019. Contains 321422 sequences. (Running on oeis4.)