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

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A328325 Expansion of Product_{k>=0} 1/(1 - x^(k^k)). 2
1, 2, 3, 4, 6, 8, 10, 12, 15, 18, 21, 24, 28, 32, 36, 40, 45, 50, 55, 60, 66, 72, 78, 84, 91, 98, 105, 113, 122, 131, 140, 150, 161, 172, 183, 195, 208, 221, 234, 248, 263, 278, 293, 309, 326, 343, 360, 378, 397, 416, 435, 455, 476, 497, 519, 542, 566, 590, 615, 641, 668, 695 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial sums of A328301.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = Sum_{k>=0} A328301(k).

G.f.: 1/(1-x) + Sum_{n>0} x^(n^n) / Product_{k=0..n} (1 - x^(k^k)).

EXAMPLE

G.f.: 1/(1-x) + x/(1-x)^2 + x^4/((1-x)^2*(1-x^4)) + x^27/((1-x)^2*(1-x^4)*(1-x^27)) + ... .

MAPLE

b:= proc(n, i) option remember; `if`(n=0 or i=1, 1,

      b(n, i-1)+(p-> `if`(p>n, 0, b(n-p, i)))(i^i))

    end:

a:= proc(n) option remember; `if`(n<2, n+1, a(n-1)+

      b(n, floor((t-> t/LambertW(t))(log(n)))))

    end:

seq(a(n), n=0..100);  # Alois P. Heinz, Oct 12 2019

PROG

(PARI) N=99; x='x+O('x^N); m=1; while(N>=m^m, m++); Vec(1/prod(k=0, m-1, 1-x^k^k))

CROSSREFS

Cf. A000312, A064985, A086858, A328301.

Sequence in context: A019293 A130519 A001972 * A005705 A139542 A238616

Adjacent sequences:  A328322 A328323 A328324 * A328326 A328327 A328328

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Oct 12 2019

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 January 23 07:07 EST 2020. Contains 331168 sequences. (Running on oeis4.)