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A365014
E.g.f. satisfies A(x) = exp( x*A(x)^2/(1 - x * A(x)^3) ).
1
1, 1, 7, 103, 2349, 72961, 2874793, 137399487, 7724650601, 499542475105, 36532938744621, 2981405776356679, 268605245211618637, 26480489709604968129, 2835590837094928349921, 327748240537910056251151, 40669893396736296241364817, 5392699633877586027282801217
OFFSET
0,3
LINKS
FORMULA
a(n) = n! * Sum_{k=0..n} (3*n-k+1)^(k-1) * binomial(n-1,n-k)/k!.
MATHEMATICA
Array[#!*Sum[ (3 # - k + 1)^(k - 1)*Binomial[# - 1, # - k]/k!, {k, 0, #}] &, 18, 0] (* Michael De Vlieger, Aug 18 2023 *)
PROG
(PARI) a(n) = n!*sum(k=0, n, (3*n-k+1)^(k-1)*binomial(n-1, n-k)/k!);
CROSSREFS
Sequence in context: A274670 A188946 A368440 * A234292 A357347 A177752
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 15 2023
STATUS
approved