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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 11 2011
STATUS
approved