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A141367 G.f.: Sum_{n>=0} arcsinh(4^n*x)^n/n!, a power series in x having only integer coefficients. 2
1, 4, 128, 43680, 178946048, 9382409745280, 6558834518571089920, 62879485860387254833099776, 8439542720341303996200869198561280, 16110026846830031883594370688522189192189952 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = [x^n] [ sqrt(1+x^2) + x ]^(4^n).
More generally, the following coefficient of x^n in the series:
[x^n] Sum_{n>=0} arcsinh(q^n*x)^n/n! = [x^n] [ sqrt(1+x^2) + x ]^(q^n) is an integer for any even integer q.
EXAMPLE
G.f.: A(x) = 1 + 4*x + 128*x^2 + 43680*x^3 + 178946048*x^4 + ...
MATHEMATICA
Table[SeriesCoefficient[(Sqrt[1 + x^2] + x)^(4^n), {x, 0, n}], {n, 0, 25}] (* G. C. Greubel, Apr 15 2017 *)
PROG
(PARI) {a(n)=polcoeff(sum(k=0, n, asinh(4^k*x +x*O(x^n))^k/k!), n)}
(PARI) {a(n)=polcoeff((x+sqrt(1+x^2 +x*O(x^n)))^(4^n), n)}
CROSSREFS
Sequence in context: A130318 A000318 A229385 * A141368 A146555 A305568
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 02 2008
STATUS
approved

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Last modified July 25 01:41 EDT 2024. Contains 374585 sequences. (Running on oeis4.)