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%I #20 Jan 24 2023 05:34:57
%S 1,8,71,778,12125,284012,9241891,378595022,18409947641,1029827400400,
%T 64998958518719,4565303338264082,353016345110857429,
%U 29793105387299603252,2724646021507044539675,268374407984059193374678
%N Expansion of e.g.f. exp(7*x)/(1-7*x)^(1/7).
%C Sum_{k = 0..n} A046716(n,k)*x^k give A000522(n), A081367(n), A094822(n), A094856(n), A094869(n), A094905(n) for x = 1, 2, 3, 4, 5, 6 respectively.
%F a(n) = Sum_{k = 0..n} A046716(n, k)*7^k.
%F Conjectured to be D-finite with recurrence: a(n) +(-7*n-1)*a(n-1) +49*(n-1)*a(n-2)=0. - _R. J. Mathar_, Nov 15 2019
%F a(n) ~ sqrt(2*Pi) * n^(n + 1/2) * 7^n / (Gamma(1/7) * exp(n-1) * n^(6/7)). - _Vaclav Kotesovec_, Nov 19 2021
%o (PARI) my(x='x+O('x^20)); Vec(serlaplace(exp(7*x)/(1-7*x)^(1/7))) \\ _Michel Marcus_, Jan 23 2023
%Y Cf. A046716, A000522, A081367, A094822, A094856, A094869, A094905.
%K nonn
%O 0,2
%A _Philippe Deléham_, Jun 17 2004
%E Corrected by _D. S. McNeil_, Aug 20 2010
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