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A104475 a(n) = binomial(n+4,4) * binomial(n+8,4).

%I A104475 #25 Mar 05 2025 03:13:36
%S A104475 70,630,3150,11550,34650,90090,210210,450450,900900,1701700,3063060,
%T A104475 5290740,8817900,14244300,22383900,34321980,51482970,75710250,
%U A104475 109359250,155405250,217567350,300450150,409704750,552210750,736281000,971890920,1270934280,1647507400,2118223800
%N A104475 a(n) = binomial(n+4,4) * binomial(n+8,4).
%H A104475 G. C. Greubel, <a href="/A104475/b104475.txt">Table of n, a(n) for n = 0..1000</a>
%H A104475 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A104475 a(n) = 70*A000581(n-8). - _Michel Marcus_, Jul 31 2015
%F A104475 From _Amiram Eldar_, Aug 30 2022: (Start)
%F A104475 Sum_{n>=0} 1/a(n) = 4/245.
%F A104475 Sum_{n>=0} (-1)^n/a(n) = 512*log(2)/35 - 37216/3675. (End)
%F A104475 From _G. C. Greubel_, Mar 05 2025: (Start)
%F A104475 G.f.: 70/(1-x)^9.
%F A104475 E.g.f.: (1/576)*(40320 + 322560*x + 564480*x^2 + 376320*x^3 + 117600*x^4 + 18816*x^5 + 1568*x^6 + 64*x^7 + x^8)*exp(x). (End)
%e A104475 a(0): C(0+4,4)*C(0+8,4) = C(4,4)*C(8,4) = 1*70 = 70.
%e A104475 a(7): C(5+4,4)*C(5+8,4) = C(9,4)*(13,4) = 126*715 = 90090.
%p A104475 A104475:=n->binomial(n+4,4)*binomial(n+8,4): seq(A104475(n), n=0..40); # _Wesley Ivan Hurt_, Jan 29 2017
%t A104475 f[n_] := Binomial[n + 4, 4]Binomial[n + 8, 4]; Table[ f[n], {n, 0, 25}] (* _Robert G. Wilson v_, Apr 20 2005 *)
%o A104475 (PARI) vector(30, n, n--; binomial(n+4,4)*binomial(n+8,4)) \\ _Michel Marcus_, Jul 31 2015
%o A104475 (Magma) [Binomial(n+4,4)*Binomial(n+8,4): n in [0..30]]; // _Vincenzo Librandi_, Jul 31 2015
%o A104475 (SageMath)
%o A104475 def A104475(n): return binomial(n+4,4)*binomial(n+8,4)
%o A104475 print([A104475(n) for n in range(31)]) # _G. C. Greubel_, Mar 05 2025
%Y A104475 Cf. A000581, A062264.
%K A104475 easy,nonn
%O A104475 0,1
%A A104475 _Zerinvary Lajos_, Apr 18 2005
%E A104475 More terms from _Robert G. Wilson v_, Apr 20 2005