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A365015
E.g.f. satisfies A(x) = exp( x*A(x)^3/(1 - x * A(x)) ).
2
1, 1, 9, 154, 3997, 140216, 6217549, 333774064, 21051514425, 1526073116032, 125040978948241, 11428407889500416, 1152792683163827413, 127215353330004610048, 15246125111980753585365, 1971966282368187450198016, 273796236099258954747416689
OFFSET
0,3
LINKS
FORMULA
a(n) = n! * Sum_{k=0..n} (n+2*k+1)^(k-1) * binomial(n-1,n-k)/k!.
MATHEMATICA
Array[#!*Sum[ (# + 2 k + 1)^(k - 1)*Binomial[# - 1, # - k]/k!, {k, 0, #}] &, 17, 0] (* Michael De Vlieger, Aug 18 2023 *)
PROG
(PARI) a(n) = n!*sum(k=0, n, (n+2*k+1)^(k-1)*binomial(n-1, n-k)/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 15 2023
STATUS
approved