The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A162506 Convergent of an infinite product, a*b*c,...; a = [1,1,1,...], b = [1,0,2,0,2,0,2,...], c = [1,0,0,3,0,0,3,0,0,3,...],... 7
 1, 1, 3, 6, 12, 23, 42, 77, 132, 236, 390, 664, 1087, 1782, 2858, 4601, 7216, 11344, 17650, 27162, 41632, 63316, 95717, 143558, 214644, 318464, 470879, 691968, 1012866, 1474434, 2140606, 3088874, 4445440, 6370142, 9095564, 12941289, 18350398, 25930984 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Equals row sums of triangle A162507. With offset 0, sum of products of parts, counted without multiplicity, in all partitions of n. Sum of products of parts, counted with multiplicity, in all partitions of n is A006906. - Vladeta Jovovic, Jul 24 2009 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 FORMULA Convergent of an infinite product, a*b*c,...; a = [1,1,1,...], b = [1,0,2,0,2,0,2,...], c = [1,0,0,3,0,0,3,0,0,3,...]; i.e. the infinite set of sequences [1,...N,...,] interleaved with (N-2) adjacent zeros. G.f.: x*Product(1+k*x^k/(1-x^k),k=1..infinity). - Vladeta Jovovic, Jul 24 2009 EXAMPLE First few rows of the array = 1,...1,...1,...1,...1,... 1,...1,...3,...3,...5,... 1,...1,...3,...6,...8,... 1,...1,...3,...6,..12,... 1,...1,...3,...6,..12,... ...tending to A162506: (1, 1, 3, 6, 12, 23, 42, 77, 132,...) MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, b(n, i-1) +add(b(n-i*j, i-1)*i, j=1..n/i))) end: a:= n-> b(n-1, n-1): seq(a(n), n=1..50); # Alois P. Heinz, Feb 26 2013 MATHEMATICA nmax = 50; Rest[CoefficientList[Series[x*Product[1+k*x^k/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jan 08 2016 *) CROSSREFS Cf. A162507, A267007. Sequence in context: A174201 A327546 A181844 * A328609 A227681 A055244 Adjacent sequences: A162503 A162504 A162505 * A162507 A162508 A162509 KEYWORD nonn AUTHOR Gary W. Adamson, Jul 04 2009 EXTENSIONS More terms from Vladeta Jovovic, Jul 22 2009 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 May 28 18:29 EDT 2024. Contains 372919 sequences. (Running on oeis4.)