|
%I #15 Oct 01 2023 12:32:54
%S 1,55,2200,71500,2002000,50050000,1144000000,24310000000,486200000000,
%T 9237800000000,167960000000000,2939300000000000,49742000000000000,
%U 817190000000000000,13075040000000000000,204297500000000000000
%N Expansion of (-1 + 1/(1-10*x)^10)/(100*x); related to A053109.
%C This is the tenth member of the k-family of sequences a(k,n) := k^(n-1)*binomial(n+k,k-1) starting with A000012 (powers of 1), A001792, A036068, A036070, A036083, A036224, A053110-113 for k=1..10.
%H G. C. Greubel, <a href="/A053113/b053113.txt">Table of n, a(n) for n = 0..400</a>
%H W. Lang, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/LANG/lang.html">On generalizations of Stirling number triangles</a>, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (100, -4500, 120000, -2100000, 25200000, -210000000, 1200000000, -4500000000, 10000000000, -10000000000).
%F a(n) = 10^(n-1)*binomial(n+10, 9).
%F G.f.: (-1 + (1-10*x)^(-10))/(x*10^2).
%t Table[10^(n - 1)*Binomial[n + 10, 9], {n, 0, 30}] (* _G. C. Greubel_, Aug 16 2018 *)
%o (PARI) vector(30,n,n--; 10^(n-1)*binomial(n+10, 9)) \\ _G. C. Greubel_, Aug 16 2018
%o (Magma) [10^(n-1)*Binomial(n+10, 9): n in [0..30]]; // _G. C. Greubel_, Aug 16 2018
%K easy,nonn
%O 0,2
%A _Wolfdieter Lang_
|
