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 A211892 G.f.: exp( Sum_{n>=1} 3 * Jacobsthal(n^2) * x^n/n ), where Jacobsthal(n) = A001045(n). 4
 1, 3, 12, 198, 16962, 6762210, 11473594848, 80455865485692, 2306084412391039038, 268657100633050977422322, 126765866001055606588876061400, 241678197713843578271875740922972788, 1858396158245858742065123341776166504084452 (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.: (1+x) * exp( Sum_{n>=1} 2^(n^2) * x^n/n ). a(n) = A155200(n) + A155200(n-1). EXAMPLE G.f.: A(x) = 1 + 3*x + 12*x^2 + 198*x^3 + 16962*x^4 + 6762210*x^5 +... such that log(A(x))/3 = x + 5*x^2/2 + 171*x^3/3 + 21845*x^4/4 + 11184811*x^5/5 + 22906492245*x^6/6 + 187649984473771*x^7/7 +...+ Jacobsthal(n^2)*x^n/n +... Jacobsthal numbers begin: A001045 = [1,1,3,5,11,21,43,85,171,341,683,1365,2731,5461,10923,21845,...]. 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^2)*x^k/k)+x*O(x^n)), n)} for(n=0, 16, print1(a(n), ", ")) CROSSREFS Cf. A211893, A211894, A211895, A211896, A207972, A001045, A155200. Cf. A231279 (Jacobsthal(n^2)). Sequence in context: A061960 A120606 A089428 * A063801 A160320 A321603 Adjacent sequences:  A211889 A211890 A211891 * A211893 A211894 A211895 KEYWORD nonn AUTHOR Paul D. Hanna, Apr 24 2012 STATUS approved

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Last modified July 24 11:17 EDT 2021. Contains 346273 sequences. (Running on oeis4.)