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 A211893 G.f.: exp( Sum_{n>=1} 3 * Jacobsthal(n)^n * x^n/n ), where Jacobsthal(n) = A001045(n). 5
 1, 3, 6, 36, 561, 98211, 43176384, 116622937722, 1022189210900601, 41675008108242048327, 6377839090284322052067558, 4114890941608928235401688095580, 10460015732506081308723488849683574907, 108482611110966450613465001912856742180485969 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Given g.f. A(x), note that A(x)^(1/3) is not an integer series. LINKS FORMULA G.f.: exp( Sum_{n>=1} (2^n - (-1)^n)^n / 3^(n-1) * x^n/n ). EXAMPLE G.f.: A(x) = 1 + 3*x + 6*x^2 + 36*x^3 + 561*x^4 + 98211*x^5 + 43176384*x^6 +... such that log(A(x))/3 = x + x^2/2 + 3^3*x^3/3 + 5^4*x^4/4 + 11^5*x^5/5 + 21^6*x^6/6 + 43^7*x^7/7 +...+ Jacobsthal(n)^n*x^n/n +... Jacobsthal numbers begin: A001045 = [1,1,3,5,11,21,43,85,171,341,683,1365,2731,5461,10923,...]. PROG (PARI) {Jacobsthal(n)=polcoeff(x/(1-x-2*x^2+x*O(x^n)), n)} {a(n)=polcoeff(exp(sum(k=1, n, 3*Jacobsthal(k)^k*x^k/k)+x*O(x^n)), n)} for(n=0, 16, print1(a(n), ", ")) CROSSREFS Cf. A211892, A211894, A211895, A211896, A207971, A207972, A001045. Cf. A231292 (Jacobsthal(n)^n). Sequence in context: A264702 A077532 A174666 * A093800 A068776 A025596 Adjacent sequences:  A211890 A211891 A211892 * A211894 A211895 A211896 KEYWORD nonn AUTHOR Paul D. Hanna, Apr 24 2012 STATUS approved

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Last modified September 24 06:13 EDT 2021. Contains 347623 sequences. (Running on oeis4.)