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 A156336 G.f.: A(x) = exp( Sum_{n>=1} 3^[(n^2+1)/2]*x^n/n ), a power series in x with integer coefficients. 2
 1, 3, 9, 99, 1917, 324567, 65546253, 121237985007, 231991261827633, 4053251131970038227, 71801958531451566872745, 11561440390042361895766055043, 1877401313066393527954697682635421 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..12. FORMULA a(n) = (1/n)*Sum_{k=1..n} 3^floor((k^2+1)/2) * a(n-k) for n>0, with a(0)=1. EXAMPLE G.f.: A(x) = 1 + 3*x + 9*x^2 + 99*x^3 + 1917*x^4 + 324567*x^5 +... log(A(x)) = 3*x + 3^2*x^2/2 + 3^5*x^3/3 + 3^8*x^4/4 + 3^13*x^5/5 + 3^18*x^6/6 +... PROG (PARI) {a(n)=polcoeff(exp(sum(k=1, n, 3^floor((k^2+1)/2)*x^k/k)+x*O(x^n)), n)} CROSSREFS Cf. A156335, A156337, A155203. Sequence in context: A185174 A018695 A250302 * A078221 A245646 A018716 Adjacent sequences: A156333 A156334 A156335 * A156337 A156338 A156339 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 10 2009 STATUS approved

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Last modified July 20 05:30 EDT 2024. Contains 374441 sequences. (Running on oeis4.)