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 A034835 #27 Aug 18 2025 02:12:26
%S A034835 1,7,196,6860,264110,10722866,450360372,19365495996,847240449825,
%T A034835 37560993275575,1682732498745760,76028913806967520,
%U A034835 3459315578217022160,158330213003009860400,7283189798138453578400,336483368673996555322080,15604416222256590253061460,726064307753233111186565580
%N A034835 Expansion of 1/(1-49*x)^(1/7); related to sept-factorial numbers A045754.
%H A034835 G. C. Greubel, <a href="/A034835/b034835.txt">Table of n, a(n) for n = 0..445</a>
%H A034835 Armin Straub, Victor H. Moll, and Tewodros Amdeberhan, <a href="http://dx.doi.org/10.4064/aa140-1-2">The p-adic valuation of k-central binomial coefficients</a>, Acta Arith. 140 (1) (2009), 31-41, eq (1.10).
%H A034835 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A034835 a(n) = 7^n*A045754(n)/n!, n >= 1, where A045754(n) = (7*n-6)(!^7) = Product_{j=1..n} (7*j-6).
%F A034835 G.f.: (1-49*x)^(-1/7).
%F A034835 D-finite with recurrence: n*a(n) + 7*(-7*n+6)*a(n-1) = 0. - _R. J. Mathar_, Jan 28 2020
%F A034835 a(n) ~ 7^(2*n) * n^(-6/7) / Gamma(1/7). - _Amiram Eldar_, Aug 18 2025
%t A034835 CoefficientList[Series[1/(1 - 49*x)^(1/7), {x,0,50}], x] (* _G. C. Greubel_, Feb 22 2018 *)
%o A034835 (PARI) my(x='x+O('x^30)); Vec(1/(1 - 49*x)^(1/7)) \\ _G. C. Greubel_, Feb 22 2018
%o A034835 (Magma) Q:=Rationals(); R<x>:=PowerSeriesRing(Q, 40); Coefficients(R!(1/(1 - 49*x)^(1/7))); // _G. C. Greubel_, Feb 22 2018
%Y A034835 Cf. A045754, A004993, A034829, A034830, A034831, A034832, A034833, A034834, A220086.
%K A034835 easy,nonn
%O A034835 0,2
%A A034835 _Wolfdieter Lang_