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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
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
Sequence in context: A174201 A327546 A181844 * A328609 A227681 A055244
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Jul 04 2009
EXTENSIONS
More terms from Vladeta Jovovic, Jul 22 2009
STATUS
approved

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Last modified May 28 18:29 EDT 2024. Contains 372919 sequences. (Running on oeis4.)