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A141367
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G.f.: Sum_{n>=0} asinh(4^n*x)^n/n!, a power series in x having only integer coefficients.
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1
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1, 4, 128, 43680, 178946048, 9382409745280, 6558834518571089920, 62879485860387254833099776, 8439542720341303996200869198561280, 16110026846830031883594370688522189192189952
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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} asinh(q^n*x)^n/n! = [x^n] [ sqrt(1+x^2) + x ]^(q^n) is an integer for any even integer q.
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EXAMPLE
| G.f.: A(x) = 1 + 4*x + 128*x^2 + 43680*x^3 + 178946048*x^4 +...
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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)}
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CROSSREFS
| Cf. A136647, A141368.
Sequence in context: A013823 A130318 A000318 * A141368 A146555 A057134
Adjacent sequences: A141364 A141365 A141366 * A141368 A141369 A141370
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jul 02 2008
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