A386274 Expansion of 1/(1 - 49*x)^(5/7).
1, 35, 1470, 65170, 2965235, 136993857, 6393046660, 300473193020, 14197358370195, 673585780452585, 32062683149543046, 1530264423046372650, 73197648235718158425, 3507856526988647130675, 168377113295455062272400, 8093326579068206659893360, 389491341617657445507367950
Offset: 0
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..592
Programs
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Mathematica
CoefficientList[Series[1/(Surd[1-49x,7])^5,{x,0,20}],x] (* Harvey P. Dale, Aug 01 2025 *) -
PARI
my(N=20, x='x+O('x^N)); Vec(1/(1-49*x)^(5/7))
Formula
a(n) = (-49)^n * binomial(-5/7,n).
a(n) = 7^n/n! * Product_{k=0..n-1} (7*k+5).
a(n) = 7^n * Product_{k=1..n} (7 - 2/k).
D-finite with recurrence n*a(n) +7*(-7*n+2)*a(n-1)=0. - R. J. Mathar, Jul 30 2025