A168365 a(n) = coefficient of x^n in the (n-1)-th iteration of Sum_{k>=0} x^(2^k), n>=1.

1, 1, 2, 12, 100, 1070, 14116, 222614, 4092964, 86058372, 2038072080, 53704876742, 1558947707912, 49437387429404, 1700708685654304, 63087246457132054, 2510333378920658240, 106666494341060615560, 4820550659164606795712

Offset

1,3

Links

Table of n, a(n) for n=1..19.

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_0: [(1), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...]
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, (86058372), ...]; ...
where the coefficients in parenthesis form the initial terms of this sequence.

Prog

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

Crossrefs

Cf. A168362, A168366.

Sequence in context: A079821 A303614 A124102 * A055865 A085389 A202013

Adjacent sequences: A168362 A168363 A168364 * A168366 A168367 A168368

Keyword

nonn

Author

Paul D. Hanna, Nov 24 2009

Status

approved