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 A188203 G.f.: exp( Sum_{n>=1} A188202(n)*x^n/n ) where A188202(n) = [x^n] (1 + 2^n*x + x^2)^n. 1
 1, 2, 11, 206, 17586, 6878604, 11551087875, 80650796495414, 2307974943300931286, 268728588584911887188180, 126776477973814964972206209838, 241684409250478693507166916367088620 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Compare to the g.f. M(x) of the Motzkin numbers (A001006): M(x) = exp( Sum_{n>=1} A002426(n)*x^n/n) where A002426(n) = [x^n] (1+x+x^2)^n. LINKS EXAMPLE G.f.: A(x) = 1 + 2*x + 11*x^2 + 206*x^3 + 17586*x^4 + 6878604*x^5 +... The l.g.f. of A188202 begins: log(A(x)) = 2*x + 18*x^2/2 + 560*x^3/3 + 68614*x^4/4 + 34210752*x^5/5 +... The coefficients of x^n in (1 + 2^n*x + x^2)^n begin: n=1: [1, (2), 1]; n=2: [1, 8, (18), 8, 1]; n=3: [1, 24, 195, (560), 195, 24, 1]; n=4: [1, 64, 1540, 16576, (68614), 16576, 1540, 64, 1]; n=5: [1, 160, 10245, 328320, 5273610, (34210752), 5273610, ...]; ... where the central coefficients form the logarithmic derivative, A188202. PROG (PARI) {a(n)=polcoeff(exp(sum(k=1, n, polcoeff((1+2^k*x+x^2+x*O(x^k))^k, k)*x^k/k)+x*O(x^n)), n)} CROSSREFS Cf. A188202 (log); variant: A001006. Sequence in context: A226052 A271429 A051663 * A070256 A020450 A036229 Adjacent sequences:  A188200 A188201 A188202 * A188204 A188205 A188206 KEYWORD nonn AUTHOR Paul D. Hanna, Mar 24 2011 STATUS approved

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Last modified June 4 02:04 EDT 2020. Contains 334812 sequences. (Running on oeis4.)