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A166922 E.g.f. exp(-x)*exp(exp(2*x)/2-1/2)/2 + 1/2. 3
1, 0, 1, 2, 10, 48, 276, 1768, 12552, 97408, 818704, 7396384, 71380640, 732058880, 7943068992, 90833753728, 1091134058624, 13728139694080, 180436251140352, 2471790031618560 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..250

R. Suter, Two analogues of a classical sequence, J. Integer Sequences, Vol. 3 (2000), #P00.1.8.

FORMULA

A004211(n) = -1 + 2*sum(k=0..n, C(n,k)*a(k)). - Peter Luschny, Nov 01 2012

G.f.: 1/2 + 1/2/Q(0), where Q(k)= 1 - 2*x*k - 2*x^2*(k+1)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, May 06 2013

MATHEMATICA

With[{nn = 25}, CoefficientList[Series[Exp[-t]*Exp[Exp[2*t]/2 - 1/2]/2 + 1/2, {t, 0, nn}], t] Range[0, nn]!] (* G. C. Greubel, May 28 2016 *)

PROG

(Sage)

def A166922_list(n):  # n>=1

    T = [0]*(n+1); R = [1]

    for m in (1..n-1):

        a, b, c = 1, 0, 0

        for k in range(m, -1, -1):

            r = a + 2*(k*(b+c)+c)

            if k < m : T[k+2] = u;

            a, b, c = T[k-1], a, b

            u = r

        T[1] = u; R.append(u/2)

    return R

A166922_list(20)

# Peter Luschny, Nov 01 2012

(PARI)x='x+O('x^66); Vec(serlaplace(exp(-x)*exp(exp(2*x)/2-1/2)/2+1/2)) \\ Joerg Arndt, May 06 2013

CROSSREFS

Sequence in context: A086853 A036918 A200540 * A302557 A129118 A037256

Adjacent sequences:  A166919 A166920 A166921 * A166923 A166924 A166925

KEYWORD

nonn

AUTHOR

Karol A. Penson, Oct 23 2009

EXTENSIONS

Definition corrected on a suggestion of M. F. Hasler, Peter Luschny, Nov 05 2012

STATUS

approved

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Last modified July 27 07:23 EDT 2021. Contains 346304 sequences. (Running on oeis4.)