cp's OEIS Frontend

A054340 10-fold convolution of A000302 (powers of 4).

%I A054340 #29 Mar 27 2022 02:39:46
%S A054340 1,40,880,14080,183040,2050048,20500480,187432960,1593180160,
%T A054340 12745441280,96865353728,704475299840,4931327098880,33381291130880,
%U A054340 219362770288640,1403921729847296,8774510811545600,53679360258867200,322076161553203200,1898554215471513600
%N A054340 10-fold convolution of A000302 (powers of 4).
%C A054340 With a different offset, number of n-permutations (n>=9) of 5 objects: u, v, z, x, y with repetition allowed, containing exactly nine (9) u's. - _Zerinvary Lajos_, Jul 02 2008
%H A054340 Vincenzo Librandi, <a href="/A054340/b054340.txt">Table of n, a(n) for n = 0..400</a>
%H A054340 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (40,-720,7680,-53760,258048,-860160,1966080,-2949120,2621440,-1048576).
%F A054340 a(n) = binomial(n+9, 9)*4^n.
%F A054340 G.f.: 1/(1 - 4*x)^10.
%F A054340 a(n) = A054335(n+19, 19).
%F A054340 E.g.f.: (2^7/9!)*(2835 + 102060*x + 816480*x^2 + 2540160*x^3 + 3810240*x^4 + 3048192*x^5 + 1354752*x^6 + 331776*x^7 + 41472*x^8 + 2048*x^9)*exp(4*x).
%F A054340 From _Amiram Eldar_, Mar 27 2022: (Start)
%F A054340 Sum_{n>=0} 1/a(n) = 236196*log(4/3) - 4756383/70.
%F A054340 Sum_{n>=0} (-1)^n/a(n) = 14062500*log(5/4) - 43931373/14. (End)
%p A054340 seq(binomial(n+9,9)*4^n,n=0..20); # _Zerinvary Lajos_, Jul 02 2008
%t A054340 Table[4^n*Binomial[n+9,9], {n,0,20}] (* _G. C. Greubel_, Jul 21 2019 *)
%o A054340 (Magma) [4^n*Binomial(n+9, 9): n in [0..20]]; // _Vincenzo Librandi_, Oct 15 2011
%o A054340 (PARI) vector(20, n, n--; 4^n*binomial(n+9, 9)) \\ _G. C. Greubel_, Jul 21 2019
%o A054340 (GAP) List([0..20], n-> 4^n*Binomial(n+9, 9)); # _G. C. Greubel_, Jul 21 2019
%Y A054340 Cf. A000302, A054335.
%K A054340 easy,nonn
%O A054340 0,2
%A A054340 _Wolfdieter Lang_, Mar 13 2000