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A206177 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n,k)^3 * 2^k ).

%I A206177 #12 Apr 23 2025 11:17:16
%S A206177 1,3,15,93,657,5067,41579,357297,3181305,29133387,272939679,
%T A206177 2605588317,25269158105,248367451299,2469462766347,24800305889217,
%U A206177 251258730935697,2565372042688563,26373806952805519,272818956588097341,2837840577104379201,29667671262881320347
%N A206177 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n,k)^3 * 2^k ).
%C A206177 Logarithmic derivative yields A206178.
%H A206177 Vaclav Kotesovec, <a href="/A206177/b206177.txt">Table of n, a(n) for n = 0..940</a>
%e A206177 G.f.: A(x) = 1 + 3*x + 15*x^2 + 93*x^3 + 657*x^4 + 5067*x^5 + 41579*x^6 +...
%e A206177 where
%e A206177 log(A(x)) = 3*x + 21*x^2/2 + 171*x^3/3 + 1521*x^4/4 + 14283*x^5/5 + 138909*x^6/6 +...+ A206178(n)*x^n/n +...
%o A206177 (PARI) {a(n)=polcoeff(exp(sum(m=1,n,x^m/m*sum(k=0,m,binomial(m,k)^3*2^k))+x*O(x^n)),n)}
%Y A206177 Cf. A206178.
%K A206177 nonn
%O A206177 0,2
%A A206177 _Paul D. Hanna_, Feb 04 2012