login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A073707 Coefficients of a power series whose convolution consists of only the even-indexed terms of the sequence. 6
1, 1, 2, 2, 5, 5, 8, 8, 18, 18, 28, 28, 50, 50, 72, 72, 129, 129, 186, 186, 301, 301, 416, 416, 664, 664, 912, 912, 1368, 1368, 1824, 1824, 2730, 2730, 3636, 3636, 5234, 5234, 6832, 6832, 9788, 9788, 12744, 12744, 17724, 17724, 22704, 22704, 31506, 31506 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Reinhard Zumkeller (confirmed by Paul D. Hanna), Table of n, a(n) for n = 0..10000

FORMULA

G.f.: A(x) satisfies A(x) = (1+x)*A(x^2)^2, with A(0)=1.

G.f.: A(x) = Product_{n>=0} (1 + x^(2^n))^(2^n).

EXAMPLE

(1 + x + 2x^2 + 2x^3 + 5x^4 + 5x^5 + 8x^6 + 8x^7 + 28x^8 + 28x^9 + ...)^2 = (1 + 2x + 5x^2 + 8x^3 + 18x^4 + 28x^5 + 50x^6 + 72x^7 + 129x^8 + ...).

MATHEMATICA

nmax = 49; CoefficientList[ Series[ Product[ (1+x^(2^n))^(2^n), {n, 0, Log[nmax]/Log[2]}], {x, 0, nmax}], x] (* Jean-Fran├žois Alcover, Jan 04 2013, from 2nd formula, modified by Vaclav Kotesovec, Oct 23 2020 *)

PROG

(PARI) a(n)=local(A, m); if(n<0, 0, m=1; A=1+O(x); while(m<=n, m*=2; A=(1+x)*subst(A, x, x^2)^2); polcoeff(A, n))

(PARI) {a(n)=polcoeff(prod(k=0, #binary(n), (1+x^(2^k)+x*O(x^n))^(2^k)), n)}

(Haskell)

a073707 n = a073707_list !! n

a073707_list = 1 : f 0 0 [1] where

   f x y zs = z : f (x + y) (1 - y) (z:zs) where

     z = sum $ zipWith (*) hzs (reverse hzs) where hzs = drop x zs

-- Reinhard Zumkeller, Dec 21 2011

CROSSREFS

Cf. A073708, A073709.

Sequence in context: A168236 A035624 A340223 * A238945 A340572 A091609

Adjacent sequences:  A073704 A073705 A073706 * A073708 A073709 A073710

KEYWORD

easy,nonn

AUTHOR

Paul D. Hanna, Aug 04 2002

EXTENSIONS

Definition corrected by Paul D. Hanna, Feb 25 2010

Data fixed for n>45 by Reinhard Zumkeller, Dec 21 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 16:15 EDT 2021. Contains 348174 sequences. (Running on oeis4.)