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A037205 a(n) = (n+1)^n - 1. 12
0, 1, 8, 63, 624, 7775, 117648, 2097151, 43046720, 999999999, 25937424600, 743008370687, 23298085122480, 793714773254143, 29192926025390624, 1152921504606846975, 48661191875666868480, 2185911559738696531967, 104127350297911241532840, 5242879999999999999999999, 278218429446951548637196400, 15519448971100888972574851071 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For n >= 1, a(n) = order of Fibonacci group F(n+1,n).

The terms, written in base n+1, are n digits of value n. For example, a(4) = 624 = 4444 in base 5. - Marc Morgenegg, Nov 30 2016

REFERENCES

D. L. Johnson, Presentation of Groups, Cambridge, 1976, p. 182.

Thomas, Richard M., The Fibonacci groups revisited, in Groups - St. Andrews 1989, Vol. 2, 445-454, London Math. Soc. Lecture Note Ser., 160, Cambridge Univ. Press, Cambridge, 1991.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..385

FORMULA

a(n) = A000169(n+1) - 1 = A060072(n+1)*(n-1) = A060073(n+1)*(n-1)^2.

E.g.f.: 1/(exp(LambertW(-x)) - x) - exp(x). - Ilya Gutkovskiy, Nov 30 2016

E.g.f.: -exp(x) - 1/(x + x/LambertW(-x)). - Vaclav Kotesovec, Dec 05 2016

MATHEMATICA

Table[(n + 1)^n - 1, {n, 0, 21}] (* or *)

Table[If[n < 1, Length@ #, FromDigits[#, n + 1]] &@ ConstantArray[n, n], {n, 0, 21}] (* Michael De Vlieger, Nov 30 2016 *)

PROG

(PARI) for(n=0, 25, print1((n + 1)^n - 1, ", ")) \\ G. C. Greubel, Nov 10 2017

(MAGMA) [(n + 1)^n - 1: n in [0..25]]; // G. C. Greubel, Nov 10 2017

CROSSREFS

A diagonal of A202624.

Sequence in context: A243782 A105219 A060071 * A302399 A084096 A189943

Adjacent sequences:  A037202 A037203 A037204 * A037206 A037207 A037208

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Revised by N. J. A. Sloane, Dec 30 2011

STATUS

approved

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Last modified December 8 18:37 EST 2019. Contains 329865 sequences. (Running on oeis4.)