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%I #5 Jun 07 2021 14:55:42
%S 1,7,63,609,6349,70693,835051,10408335,136290371,1867933865,
%T 26712000161,397487932457,6140285212915,98264596199651,
%U 1626101133819855,27779382241071769,489188555650420493,8867962363328434205,165284825277198034611,3163858565498874214559,62133992974174011252635
%N a(0) = 1; a(n) = 7 * Sum_{k=1..n} binomial(n,k) * a(k-1).
%F G.f. A(x) satisfies: A(x) = 1 + 7 * x * A(x/(1 - x)) / (1 - x)^2.
%t a[0] = 1; a[n_] := a[n] = 7 Sum[Binomial[n, k] a[k - 1], {k, 1, n}]; Table[a[n], {n, 0, 20}]
%t nmax = 20; A[_] = 0; Do[A[x_] = 1 + 7 x A[x/(1 - x)]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y Cf. A040027, A144263, A238464, A343523, A343975, A344735, A344840, A345077, A345081.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Jun 07 2021