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A064757
a(n) = n*11^n - 1.
5
10, 241, 3992, 58563, 805254, 10629365, 136410196, 1714871047, 21221529218, 259374246009, 3138428376720, 37661140520651, 448795257871102, 5316497670165373, 62658722541234764, 735195677817154575, 8592599484487994106, 100078511642860166657, 1162022718519876379528
OFFSET
1,1
COMMENTS
Conjecture: satisfies a linear recurrence having signature (23,-143,121). - Harvey P. Dale, May 12 2019
This conjecture is true since a(n) - a(n-1) yields the recurrence 1 + 10*n + 11*n*a(n-1) - (n-1)*a(n) = 0 with polynomial coefficients in n. - Georg Fischer, Feb 19 2021
FORMULA
From Elmo R. Oliveira, Sep 07 2024: (Start)
G.f.: x*(121*x^2 - 11*x - 10)/((x - 1)*(11*x - 1)^2).
E.g.f.: 1 + exp(x)*(11*x*exp(10*x) - 1).
a(n) = 23*a(n-1) - 143*a(n-2) + 121*a(n-3) for n > 3.
a(n) = A064749(n) - 2. (End)
MAPLE
k:= 11; f:= gfun:-rectoproc({1 + (k-1)*n + k*n*a(n-1) - (n-1)*a(n) = 0, a(1) = k-1}, a(n), remember): map(f, [$1..20]); # Georg Fischer, Feb 19 2021
MATHEMATICA
Table[n*11^n-1, {n, 20}] (* Harvey P. Dale, May 12 2019 *)
PROG
(Magma) [n*11^n - 1: n in [1..20]]; // Vincenzo Librandi, Sep 16 2011
CROSSREFS
Cf. for a(n) = n*k^n - 1: -A000012(k=0), A001477(k=1), A003261 (k=2), A060352 (k=3), A060416 (k=4), A064751 (k=5), A064752 (k=6), A064753 (k=7), A064754 (k=8), A064755 (k=9), A064756 (k=10), this sequence (k=11), A064758 (k=12).
Cf. A064749.
Sequence in context: A171204 A156443 A211088 * A087435 A331611 A122836
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 19 2001
STATUS
approved