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A206153 G.f.: exp( Sum_{n>=1} A206154(n)*x^n/n ), where A206154(n) = Sum_{k=0..n} binomial(n,k)^(k+2).

%I A206153 #10 Feb 20 2025 14:05:36
%S A206153 1,2,7,48,693,26632,2542514,533442978,278979307990,343728261289376,
%T A206153 904762216681139381,5771110378770242683658,88742047516327429085056353,
%U A206153 2912737209806573079629325613400,224604736339682169442980060945290802
%N A206153 G.f.: exp( Sum_{n>=1} A206154(n)*x^n/n ), where A206154(n) = Sum_{k=0..n} binomial(n,k)^(k+2).
%C A206153 Logarithmic derivative yields A206154.
%e A206153 G.f.: A(x) = 1 + 2*x + 7*x^2 + 48*x^3 + 693*x^4 + 26632*x^5 + 2542514*x^6 +...
%e A206153 where the logarithm of the g.f. begins:
%e A206153 log(A(x)) = 2*x + 10*x^2/2 + 110*x^3/3 + 2386*x^4/4 + 125752*x^5/5 + 14921404*x^6/6 +...+ A206154(n)*x^n/n +...
%o A206153 (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,x^m/m*sum(k=0,m,binomial(m,k)^(k+2))+x*O(x^n))),n)}
%o A206153 for(n=0,16,print1(a(n),", "))
%Y A206153 Cf. A206154 (log), A184730, A206155, A206157, A206151.
%K A206153 nonn
%O A206153 0,2
%A A206153 _Paul D. Hanna_, Feb 04 2012