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A105940 a(n) = binomial(n+5, 5)*binomial(n+8, 5).

%I A105940 #27 Mar 11 2025 04:37:52
%S A105940 56,756,5292,25872,99792,324324,924924,2378376,5621616,12388376,
%T A105940 25729704,50791104,95938752,174350232,306211752,521694096,864913896,
%U A105940 1399125420,2213431220,3431347920,5221616400,7811703900,11504509380,16698853080,23914406880,33821804016
%N A105940 a(n) = binomial(n+5, 5)*binomial(n+8, 5).
%H A105940 T. D. Noe, <a href="/A105940/b105940.txt">Table of n, a(n) for n = 0..1000</a>
%H A105940 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F A105940 G.f.: 28*(2+x)*(1+2*x) / (1-x)^11. - _Colin Barker_, Jan 28 2013
%F A105940 From _Amiram Eldar_, Sep 01 2022: (Start)
%F A105940 Sum_{n>=0} 1/a(n) = 580367/1764 - 100*Pi^2/3.
%F A105940 Sum_{n>=0} (-1)^n/a(n) = 74537/588 - 1280*log(2)/7. (End)
%e A105940 a(0) = C(0+5,0)*C(0+8,5) = C(5,0)*C(8,5) = 1*56 = 56
%e A105940 a(6) = C(6+5,6)*C(6+8,5) = C(11,6)*C(14,5) = 462*2002 = 924924.
%p A105940 with(combinat); for i from 0 to 25 do print(i,numbcomb(i+5,i)*numbcomb(i+8,5)); end; # _Jim Nastos_, Oct 26 2005
%t A105940 a[n_] := Binomial[n + 5, 5] * Binomial[n + 8, 5]; Array[a, 25, 0] (* _Amiram Eldar_, Sep 01 2022 *)
%o A105940 (Magma)
%o A105940 A105940:= func< n | Binomial(n+5,5)*Binomial(n+8,5) >;
%o A105940 [A105940(n): n in [0..40]]; // _G. C. Greubel_, Mar 11 2025
%o A105940 (SageMath)
%o A105940 def A105940(n): return binomial(n+5,5)*binomial(n+8,5)
%o A105940 print([A105940(n) for n in range(41)]) # _G. C. Greubel_, Mar 11 2025
%Y A105940 Cf. A062145.
%K A105940 easy,nonn
%O A105940 0,1
%A A105940 _Zerinvary Lajos_, Apr 27 2005
%E A105940 More terms from _Jim Nastos_, Oct 26 2005