A172362 - OEIS

%I #21 Aug 28 2022 04:22:27

%S 1,33,594,7722,81081,729729,5837832,42532776,287096238,1818276174,

%T 10909657044,62482581252,343654196886,1824010737318,9380626649064,

%U 46903133245320,228652774570935,1089463220014455,5084161693400790

%N a(n) = binomial(n+10, 10)*3^n.

%C With a different offset, number of n-permutations (n>=10) of 4 objects: u, v, z, x with repetition allowed, containing exactly ten, (10) u's.

%H Vincenzo Librandi, <a href="/A172362/b172362.txt">Table of n, a(n) for n = 0..400</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (33,-495,4455,-26730,112266,-336798,721710,-1082565,1082565,-649539,177147).

%F G.f.: 1/(1-3*x)^11. - _Vincenzo Librandi_, Oct 15 2011

%F From _Amiram Eldar_, Aug 28 2022: (Start)

%F Sum_{n>=0} 1/a(n) = 261617/42 - 15360*log(3/2).

%F Sum_{n>=0} (-1)^n/a(n) = 7864320*log(4/3) - 47510881/21. (End)

%p seq(binomial(n+10, 10)*3^n, n=0..30);

%t Table[Binomial[n + 10, 10]*3^n, {n, 0, 20}]

%o (Magma) [3^n*Binomial(n+10, 10): n in [0..30]]; // _Vincenzo Librandi_, Oct 15 2011

%Y Cf. A027472, A036216, A036217, A036219, A036220, A036221, A036222, A036223.

%K nonn,easy

%O 0,2

%A _Zerinvary Lajos_, Feb 01 2010