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A084978 Number of ways to represent n as a+b*(c+d*(e+f*(...x+y*(z)...))) in positive integers. 0
1, 2, 5, 11, 25, 51, 110, 221, 456, 918, 1864, 3729, 7528, 15057, 30227, 60485, 121205, 242411, 485337, 970675, 1942307, 3884730, 7771327, 15542655, 31089330, 62178686, 124364903, 248730268, 497475717, 994951435, 1989934099, 3979868199 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..32.

FORMULA

a(n+1) = Sum(k=1..n; Sum(d|k; a(d)).

a(n+1) = 1 + Sum(k=1..n; Sum(d|k; a(d)) or a(n+1) = a(n) + Sum(d|n; a(d)). - Vladeta Jovovic, Aug 08 2004

G.f. A(x) satisfies: A(x) = (x/(1 - x)) * (1 + Sum_{k>=1} A(x^k)). - Ilya Gutkovskiy, Feb 25 2020

EXAMPLE

a(3) = 5: 3 = 2+1(1) = 1+2(1) = 1+1(2) = 1+1(1+1(1)).

CROSSREFS

Sequence in context: A134527 A124379 A302830 * A118036 A291552 A208739

Adjacent sequences:  A084975 A084976 A084977 * A084979 A084980 A084981

KEYWORD

nonn

AUTHOR

David W. Wilson, Jun 16 2003

STATUS

approved

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Last modified April 23 10:07 EDT 2021. Contains 343204 sequences. (Running on oeis4.)