A365013 E.g.f. satisfies A(x) = exp( x*A(x)/(1 - x * A(x)^3) ).

1, 1, 5, 58, 1061, 26536, 843457, 32553424, 1478813513, 77304347776, 4571222616701, 301696674682624, 21985118975444077, 1753288356936334336, 151887264799071753785, 14203597499192539334656, 1426051485043745729079953, 153000280727938469281693696

Offset: 0

Author

Seiichi Manyama, Aug 15 2023

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..341

Crossrefs

Cf. A052873, A365012.

Programs

Mathematica

Array[#!*Sum[ (3 # - 2 k + 1)^(k - 1)*Binomial[# - 1, # - k]/k!, {k, 0, #}] &, 18, 0] (* Michael De Vlieger, Aug 18 2023 *)

PARI

a(n) = n!*sum(k=0, n, (3*n-2*k+1)^(k-1)*binomial(n-1, n-k)/k!);

Formula

a(n) = n! * Sum_{k=0..n} (3*n-2*k+1)^(k-1) * binomial(n-1,n-k)/k!.