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A276371 E.g.f.: exp(x/2)/(2 - exp(2*x))^(1/4). 1
1, 1, 3, 19, 177, 2161, 32643, 587539, 12273537, 291853441, 7782998883, 230028553459, 7462717994097, 263654454838321, 10075889406229923, 414147167601017779, 18217983822073897857, 853975145498805244801, 42495107452208870429763, 2237264405984004517212499, 124243242448367338311920817, 7258224393227482972980320881, 444967879322677755285771182403, 28563002475012109334240250609619 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Paul D. Hanna, Table of n, a(n) for n = 0..520

FORMULA

E.g.f. A(x) satisfies: A'(x) = A(x)*(1 + A(x)^4)/2 with A(0)=1.

a(2*n) = 0 (mod 3), a(2*n+1) = 1 (mod 3), for n>=0.

a(n) ~ Gamma(3/4) * 2^n * n^(n-1/4) / (sqrt(Pi) * exp(n) * (log(2))^(n+1/4)). - Vaclav Kotesovec, Sep 11 2016

EXAMPLE

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 19*x^3/3! + 177*x^4/4! + 2161*x^5/5! + 32643*x^6/6! + 587539*x^7/7! + 12273537*x^8/8! + 291853441*x^9/9! + 7782998883*x^10/10! +...

such that A(x) = exp(x/2)/(2 - exp(2*x))^(1/4).

MATHEMATICA

With[{nn = 50}, CoefficientList[Series[Exp[x/2]/(2 - Exp[2*x])^(1/4), {x, 0, nn}], x] Range[0, nn]!] (* G. C. Greubel, Apr 09 2017 *)

PROG

(PARI) {a(n)=local(A=1+x, X=x+x*O(x^n)); A = exp(X/2)/(2-exp(2*X))^(1/4); n!*polcoeff(A, n)}

for(n=0, 30, print1(a(n), ", "))

CROSSREFS

Sequence in context: A305459 A045531 A129481 * A156131 A269421 A304578

Adjacent sequences:  A276368 A276369 A276370 * A276372 A276373 A276374

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 09 2016

STATUS

approved

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Last modified November 20 02:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)