This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A034256 #20 Aug 19 2025 05:21:02
%S A034256 1,4,24,224,2464,29568,374528,4922368,66451968,915560448,12817846272,
%T A034256 181780365312,2605518569472,37679807004672,549048616353792,
%U A034256 8052713039855616,118777517337870336,1760702021714313216,26214896767746441216,391843720107367858176,5877655801610517872640
%N A034256 Expansion of 2 - (1 - 16*x)^(1/4), related to quartic factorial numbers A034176.
%F A034256 Equals 4 * A025749(n), n > 0.
%F A034256 a(n) = 4^n*3*A034176(n-1)/n!, n >= 2, where 3*A034176(n-1) = (4*n-5)(!^4) = Product_{j=2..n} (4*j - 5).
%F A034256 O.g.f.: A(x) = 2 - (1 - 16*x)^(1/4).
%F A034256 From _Peter Bala_, Nov 19 2015: (Start)
%F A034256 For n >= 1, a(n) = (1/(sqrt(2)*Pi)) * Integral_{x = 0..16} x^(n-1)*((16 - x)/x)^(1/4) dx.
%F A034256 It appears that sqrt(A(x)) = 1 + 2*x + 10*x^2 + 92*x^3 + 998*x^4 + 11868*x^5 + 149316*x^6 + ... has integer coefficients. (End)
%F A034256 a(n) ~ 4^(2*n-1) * n^(-5/4) / Gamma(3/4). - _Amiram Eldar_, Aug 19 2025
%t A034256 a[n_] := 4^(2*n-1)*Pochhammer[3/4, n-1]/n!; a[0] = 1; Array[a, 25, 0] (* _Amiram Eldar_, Aug 19 2025 *)
%Y A034256 Cf. A025749, A034176, A068465.
%K A034256 easy,nonn
%O A034256 0,2
%A A034256 _Wolfdieter Lang_
%E A034256 More terms from _Amiram Eldar_, Aug 19 2025