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 A159597 G.f.: A(x) = exp( Sum_{n>=1} [ D^n x/(1-x)^3 ]^n/n ), where differential operator D = x*d/dx. 2
 1, 1, 7, 37, 245, 2094, 24661, 410376, 9809637, 334520167, 16192227784, 1107914634442, 106788033119369, 14525652771018918, 2780328926392863928, 751651711717655433750, 286240041470280077141769 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..16. FORMULA G.f.: A(x) = exp( Sum_{n>=1} [Sum_{k>=1} k^n*k(k+1)/2*x^k]^n/n ) where A(x) = Sum_{k>=1} a(k)*x^k. EXAMPLE G.f.: A(x) = 1 + x + 7*x^2 + 37*x^3 + 245*x^4 + 2094*x^5 +... log(A(x)) = Sum_{n>=1} [x + 2^n*3*x^2 + 3^n*6*x^3 +...]^n/n. D^n x/(1-x)^3 = x + 2^n*3*x^2 + 3^n*6*x^3 + 4^n*10*x^4 +... PROG (PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sum(k=1, n, k^m*k*(k+1)/2*x^k+x*O(x^n))^m/m))); polcoeff(A, n)} CROSSREFS Cf. A156170, A159596, A159598. Sequence in context: A332906 A361279 A096965 * A217723 A100309 A198410 Adjacent sequences: A159594 A159595 A159596 * A159598 A159599 A159600 KEYWORD nonn AUTHOR Paul D. Hanna, May 05 2009 STATUS approved

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Last modified July 21 11:45 EDT 2024. Contains 374472 sequences. (Running on oeis4.)