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%I #5 Mar 30 2012 18:37:35
%S 1,2,7,102,6261,2423430,6686021554,61335432894584,2941073857435300366,
%T 1190520035262419577871332,1696475310227140760623646031573,
%U 9980324833243234634513255755001535870,565171444566758371735408026461987217216896790
%N G.f.: exp( Sum_{n>=1} A206158(n)*x^n/n ), where A206158(n) = Sum_{k=0..n} binomial(n,k)^(2*k+1).
%C Logarithmic derivative yields A206158.
%e G.f.: A(x) = 1 + 2*x + 7*x^2 + 102*x^3 + 6261*x^4 + 2423430*x^5 +...
%e where the logarithm of the g.f. begins:
%e log(A(x)) = 2*x + 10*x^2/2 + 272*x^3/3 + 24226*x^4/4 + 12053252*x^5/5 + 40086916024*x^6/6 +...+ A206158(n)*x^n/n +...
%o (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,x^m/m*sum(k=0,m,binomial(m,k)^(2*k+1))+x*O(x^n))),n)}
%o for(n=0,16,print1(a(n),", "))
%Y Cf. A206158 (log), A184730, A206153, A206155, A206151.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Feb 04 2012
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