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 A218117 G.f.: A(x) = exp( Sum_{n>=1} A005261(n)*x^n/n ) where A005261(n) = Sum_{k=0..n} C(n,k)^5. 4
 1, 2, 19, 198, 2961, 49566, 938322, 19083624, 412160478, 9305822076, 217855152321, 5251363667622, 129704365956114, 3269927116717728, 83893626609970281, 2185188966488265718, 57673989852987800966, 1539973309401567102832, 41544812360973818992909 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Compare to a g.f. of Catalan numbers (A000108): exp( Sum_{n>=1} A000984(n)*x^n/n ) where A000984(n) = Sum_{k=0..n} C(n,k)^2. LINKS FORMULA Equals row sums of triangle A218115. Self-convolution of A218118. EXAMPLE G.f.: A(x) = 1 + 2*x + 19*x^2 + 198*x^3 + 2961*x^4 + 49566*x^5 + 938322*x^6 +... log(A(x)) = 2*x + 34*x^2/2 + 488*x^3/3 + 9826*x^4/4 + 206252*x^5/5 + 4734304*x^6/6 + 113245568*x^7/7 +...+ A005261(n)*x^n/n +... PROG (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^5)*x^m/m)+x*O(x^n)), n)} for(n=0, 25, print1(a(n), ", ")) CROSSREFS Cf. A218115, A218118, A166990, A166992, A218119, A005261. Sequence in context: A124262 A140781 A128970 * A145104 A114016 A268707 Adjacent sequences:  A218114 A218115 A218116 * A218118 A218119 A218120 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 21 2012 STATUS approved

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Last modified January 26 16:58 EST 2020. Contains 331280 sequences. (Running on oeis4.)