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%I #16 Sep 08 2022 08:44:52
%S 1,7,196,6860,264110,10722866,450360372,19365495996,847240449825,
%T 37560993275575,1682732498745760,76028913806967520,
%U 3459315578217022160,158330213003009860400,7283189798138453578400,336483368673996555322080
%N Expansion of 1/(1-49*x)^(1/7); related to sept-factorial numbers A045754.
%H G. C. Greubel, <a href="/A034835/b034835.txt">Table of n, a(n) for n = 0..445</a>
%H A. Straub, V. H. Moll, T. 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)
%F a(n) = 7^n*A045754(n)/n!, n >= 1, A045754(n) = (7*n-6)(!^7) := product(7*j-6, j=1..n); G.f.: (1-49*x)^(-1/7).
%F D-finite with recurrence: n*a(n) +7*(-7*n+6)*a(n-1)=0. - _R. J. Mathar_, Jan 28 2020
%t CoefficientList[Series[1/(1 - 49*x)^(1/7), {x,0,50}], x] (* _G. C. Greubel_, Feb 22 2018 *)
%o (PARI) x='x+O('x^30); Vec(1/(1 - 49*x)^(1/7)) \\ _G. C. Greubel_, Feb 22 2018
%o (Magma) Q:=Rationals(); R<x>:=PowerSeriesRing(Q, 40); Coefficients(R!(1/(1 - 49*x)^(1/7))) // _G. C. Greubel_, Feb 22 2018
%Y Cf. A045754, A004993, A034829, A034830, A034831, A034832, A034833, A034834.
%K easy,nonn
%O 0,2
%A _Wolfdieter Lang_
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