The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A308272 G.f. A(x) satisfies: A(x) = (1 + x) * A(x^2)*A(x^3)*A(x^5)* ... *A(x^prime(k))* ... 2
 1, 1, 1, 2, 2, 3, 5, 6, 7, 10, 13, 16, 22, 27, 33, 44, 53, 65, 84, 101, 124, 156, 187, 226, 280, 336, 403, 492, 587, 700, 850, 1008, 1195, 1435, 1693, 2004, 2390, 2808, 3303, 3910, 4584, 5372, 6328, 7387, 8619, 10106, 11757, 13675, 15961, 18508, 21464, 24948, 28845, 33345 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Weigh transform of A008480. LINKS Table of n, a(n) for n=0..53. FORMULA G.f.: Product_{k>=1} (1 + x^k)^A008480(k). MAPLE g:= proc(n) option remember; (l-> add(i, i=l)!/ mul(i!, i=l))(map(i-> i[2], ifactors(n)[2])) end: b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(binomial(g(i), j)*b(n-i*j, i-1), j=0..n/i))) end: a:= n-> b(n\$2): seq(a(n), n=0..60); # Alois P. Heinz, May 17 2019 MATHEMATICA terms = 53; A[_] = 1; Do[A[x_] = (1 + x) Product[A[x^Prime[k]], {k, 1, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x] CROSSREFS Cf. A000040, A008480, A129373, A308271. Sequence in context: A096981 A281966 A276431 * A035541 A187502 A236970 Adjacent sequences: A308269 A308270 A308271 * A308273 A308274 A308275 KEYWORD nonn AUTHOR Ilya Gutkovskiy, May 17 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 29 02:18 EDT 2023. Contains 365748 sequences. (Running on oeis4.)