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A195262 G.f.: A(x) = Sum_{n>=0} x^n*A(x)^A001969(n+1), where A001969 lists numbers with an even number of 1's in their binary expansion. 1
1, 1, 4, 21, 125, 805, 5459, 38403, 277667, 2050771, 15405655, 117344350, 904175038, 7035182178, 55197856415, 436221495843, 3469249248383, 27744896161177, 222987118478532, 1800106801933350, 14589674016207940, 118674224290447850, 968474133792224994 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..22.

EXAMPLE

G.f.: A(x) = 1 + x + 4*x^2 + 21*x^3 + 125*x^4 + 805*x^5 + 5459*x^6 +...

where

A(x) = 1 + x*A(x)^3 + x^2*A(x)^5 + x^3*A(x)^6 + x^4*A(x)^9 + x^5*A(x)^10 + x^6*A(x)^12 + x^7*A(x)^15 + x^8*A(x)^17 +...

and exponents A001969(n) begin:

[0,3,5,6,9,10,12,15,17,18,20,23,24,27,29,30,33,34,36,39,40,...].

PROG

(PARI) {A000120(n)=n-sum(k=1, #binary(n), floor(n/2^k))}

{A001969(n) = (1/2)*(4*n+1-(-1)^A000120(n))}

{a(n)=local(A=1+x+x*O(x^n)); for(k=1, n, A=1+sum(j=1, n, x^j*A^A001969(j))); polcoeff(A, n)}

CROSSREFS

Cf. A001969 (evil numbers), A195261.

Sequence in context: A153291 A244062 A093965 * A162480 A275758 A003168

Adjacent sequences:  A195259 A195260 A195261 * A195263 A195264 A195265

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 13 2011

STATUS

approved

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Last modified September 24 14:46 EDT 2021. Contains 347643 sequences. (Running on oeis4.)