A168366 a(n) = coefficient of x^n in the (n+1)-th iteration of Sum_{k>=0} x^(2^k), n>=1.

1, 3, 12, 75, 650, 7238, 98728, 1597689, 29965770, 639867250, 15337926824, 408041226684, 11934806334412, 380779156844728, 13163263492873152, 490208180677163141, 19568027053121979366, 833594881998712829460

Offset

1,2

Links

Table of n, a(n) for n=1..18.

Example

Let F(x) = x + x^2 + x^4 + x^8 + x^16 +...+ x^(2^n) +...
and define F_{n}(x) = F_{n-1}(x*F(x)) as the n-th iteration of F(x)
then the coefficients in the successive iterations of F(x) begin:
F_1: [1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, ...];
F_2: [(1), 2, 2, 3, 6, 8, 8, 16, 22, 40, 80, 146, 240, 356,...];
F_3: [1, (3), 6, 12, 28, 68, 152, 330, 722, 1614, 3680, 8810, ...];
F_4: [1, 4, (12), 34, 100, 310, 972, 3012, 9190, 27826, 84192,...];
F_5: [1, 5, 20, (75), 280, 1070, 4176, 16449, 64710, 253166, ...];
F_6: [1, 6, 30, 141, (650), 3010, 14116, 66972, 319788, 1529230,...];
F_7: [1, 7, 42, 238, 1316, (7238), 39984, 222614, 1248304,...];
F_8: [1, 8, 56, 372, 2408, 15428, (98728), 634040, 4092964,...];
F_9: [1, 9, 72, 549, 4080, 29940, 218688, (1597689), 11704548,...];
F_10:[1, 10, 90, 775, 6510, 53940, 443952, 3646168, (29965770),...]; ...
where the coefficients in parenthesis form the initial terms of this sequence.

Prog

(PARI) {a(n)=local(G=x, S2=sum(m=0, #binary(n)+1, x^(2^m))+x*O(x^n)); for(i=1, n+1, G=subst(S2, x, G)); polcoeff(G, n)}

Crossrefs

Cf. A168362, A168365.

Sequence in context: A176408 A238630 A247330 * A134524 A120591 A247057

Adjacent sequences: A168363 A168364 A168365 * A168367 A168368 A168369

Keyword

nonn

Author

Paul D. Hanna, Nov 24 2009

Status

approved