A345078 a(0) = 1; a(n) = 7 * Sum_{k=1..n} binomial(n,k) * a(k-1).

1, 7, 63, 609, 6349, 70693, 835051, 10408335, 136290371, 1867933865, 26712000161, 397487932457, 6140285212915, 98264596199651, 1626101133819855, 27779382241071769, 489188555650420493, 8867962363328434205, 165284825277198034611, 3163858565498874214559, 62133992974174011252635

Offset: 0

Author

Ilya Gutkovskiy, Jun 07 2021

Keywords

• nonn

Crossrefs

Cf. A040027, A144263, A238464, A343523, A343975, A344735, A344840, A345077, A345081.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = 7 Sum[Binomial[n, k] a[k - 1], {k, 1, n}]; Table[a[n], {n, 0, 20}]
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]

Formula

G.f. A(x) satisfies: A(x) = 1 + 7 * x * A(x/(1 - x)) / (1 - x)^2.