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%I #6 Jun 24 2016 23:23:05
%S 1,1,5,82,2729,151376,12567187,1457297878,224869459201,44538286061152,
%T 11011493721321251,3323602336722922574,1202633627172086804257,
%U 513869583003728865617848,255985770924976071728925555,147050140379016992236158750526,96489590122440823908683879560193,71722476615114676804476795900453248,59952692198711311645811325484552353091,55990325778560798795385664699772933184190,58081532846176563089250398770056580653829601
%N Main diagonal of rectangular array A274391 of coefficients in functions that satisfy W_n(x) = W_{n-1}(x)^W_n(x), with W_0(x) = exp(x).
%H Paul D. Hanna, <a href="/A274388/b274388.txt">Table of n, a(n) for n = 0..100</a>
%o (PARI) {ITERATE(F,n,k) = my(G=x +x*O(x^k)); for(i=1,n,G=subst(G,x,F));G}
%o {A274391(n,k) = my(TREE = serreverse(x*exp(-x +x*O(x^k)))); k!*polcoeff(exp(ITERATE(TREE,n,k)),k)}
%o /* Print table A274391 */
%o for(n=0,10,for(k=0,10,print1(A274391(n,k),", "));print("..."))
%o /* Print this sequence as the main diagonal in A274391 */
%o for(n=0,20,print1(A274391(n,n),", "))
%Y Cf. A274391, A274387, A274389.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 24 2016
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