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 A195193 G.f.: A(x) = x + x*ITERATE^2(x + 2*x*ITERATE^2(x + 3*x*ITERATE^2(x + 4*x*ITERATE^2(x + ...)))), where ITERATE^2(F(x)) = F(F(x)), and the nested iterations continue indefinitely. 1
 1, 1, 4, 32, 392, 6492, 135876, 3450048, 103437240, 3592136052, 142420085352, 6373515782544, 318952925294496, 17709716546754768, 1083721599571837632, 72661988008040494752, 5310638869813310865984, 421165309915181979699168, 36095229917026934599948992 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Paul D. Hanna, Table of n, a(n) for n = 1..100 EXAMPLE G.f.: A(x) = x + x^2 + 4*x^3 + 32*x^4 + 392*x^5 + 6492*x^6 +... where A(x) is generated by nested iterations of shifted series: A(x) = x + x*B(B(x)), where B(x) = x + 2*x^2 + 12*x^3 + 132*x^4 + 2118*x^5 + 44400*x^6 +...; B(x) = x + 2*x*C(C(x)), where C(x) = x + 3*x^2 + 24*x^3 + 336*x^4 + 6672*x^5 + 169560*x^6 +...; C(x) = x + 3*x*D(D(x)), where D(x) = x + 4*x^2 + 40*x^3 + 680*x^4 + 16100*x^5 + 481200*x^6 +...; D(x) = x + 4*x*E(E(x)), where E(x) = x + 5*x^2 + 60*x^3 + 1200*x^4 + 33000*x^5 + 1134420*x^6 +...; E(x) = x + 5*x*F(F(x)), where F(x) = x + 6*x^2 + 84*x^3 + 1932*x^4 + 60522*x^5 + 2352672*x^6 +...; E(x) = x + 6*x*G(G(x)), where G(x) = x + 7*x^2 + 112*x^3 + 2912*x^4 + 102368*x^5 + 4440240*x^6 +...; G(x) = x + 7*x*H(H(x)), where H(x) = x + 8*x^2 + 144*x^3 + 4176*x^4 + 162792*x^5 + 7794720*x^6 +...; ... Also, the 2nd iteration of the g.f. A(x) begins: A(A(x)) = x + 2*x^2 + 10*x^3 + 85*x^4 + 1044*x^5 + 16996*x^6 + 347960*x^7 + 8649376*x^8 + 254561796*x^9 + 8704440152*x^10 +... PROG (PARI) {a(n)=local(A=x); for(k=0, n, A=x + (n-k+1)*x*subst(A, x, A+x*O(x^n))); polcoeff(A, n)} CROSSREFS Sequence in context: A222412 A349601 A007763 * A203435 A349558 A005263 Adjacent sequences:  A195190 A195191 A195192 * A195194 A195195 A195196 KEYWORD nonn AUTHOR Paul D. Hanna, Sep 11 2011 STATUS approved

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Last modified June 27 16:27 EDT 2022. Contains 354896 sequences. (Running on oeis4.)