A386273 Expansion of 1/(1 - 49*x)^(4/7).
1, 28, 1078, 45276, 1980825, 88740960, 4037713680, 185734829280, 8613452707860, 401961126366800, 18851976826602920, 887756726925482960, 41946505347229069860, 1987619022607162079520, 94411903573840198777200, 4494006610114793461794720, 214307940219849213209335710
Offset: 0
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(1/(1-49*x)^(4/7))
Formula
a(n) = (-49)^n * binomial(-4/7,n).
a(n) = 7^n/n! * Product_{k=0..n-1} (7*k+4).
a(n) = 7^n * Product_{k=1..n} (7 - 3/k).
D-finite with recurrence n*a(n) +7*(-7*n+3)*a(n-1)=0. - R. J. Mathar, Jul 20 2025