A212491 G.f.: A(x) = x + x*ITERATE^2(x + x*ITERATE^4(x + x*ITERATE^8(x + x*ITERATE^16(x + ...)))), where ITERATE^n(F(x)) denotes the n-th iteration of F(x), and the nesting of iterations continue indefinitely.

1, 1, 2, 10, 109, 2344, 95526, 7321508, 1062894966, 295821381776, 159750645147982, 169055785061863986, 353149667541498542122, 1463495730873823283553016, 12070551778811708797824867546, 198534598750957942596957876692320, 6519958358404237723197281898833187776

Offset

1,3

Links

Table of n, a(n) for n=1..17.

Example

G.f.: A(x) = x + x^2 + 2*x^3 + 10*x^4 + 109*x^5 + 2344*x^6 + 95526*x^7 +...
where A(x) is generated by nesting 2^n-th iterations of shifted series:
A(x) = x + x*B(B(x));
B(x) = x + x*C(C(C(C(x))));
C(x) = x + x*D(D(D(D(D(D(D(D(x))))))));
D(x) = x + x*E(E(E(E(E(E(E(E(E(E(E(E(E(E(E(E(x)))))))))))); ...
The above series begin:
B(x) = x + x^2 + 4*x^3 + 44*x^4 + 1006*x^5 + 43392*x^6 + 3459214*x^7 +...
C(x) = x + x^2 + 8*x^3 + 184*x^4 + 8620*x^5 + 746176*x^6 + 117816292*x^7 +...
D(x) = x + x^2 + 16*x^3 + 752*x^4 + 71320*x^5 + 12374144*x^6 +...
E(x) = x + x^2 + 32*x^3 + 3040*x^4 + 580144*x^5 + 201551104*x^6 +...

Prog

(PARI) /* Define the (2^n)-th iteration of function F: */
{ITERATE2(n, F, p=#F)=local(G=F); for(i=1, n, G=subst(G, x, G+x*O(x^p))); G}
/* A(x) results from nested iterations of shifted series: */
{a(n)=local(A=x); for(k=0, n, A=ITERATE2(n-k, x + x*A, n)); polcoeff(A, n)}
for(n=1, 20, print1(a(n), ", "))

Crossrefs

Cf. A195192, A205320, A205319.

Sequence in context: A003167 A240625 A062412 * A364409 A006608 A066205

Adjacent sequences: A212488 A212489 A212490 * A212492 A212493 A212494

Keyword

nonn

Author

Paul D. Hanna, May 18 2012

Status

approved