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A370926
Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x*exp(x^3/6)) ).
2
1, 1, 2, 6, 28, 220, 2520, 34510, 519680, 8527680, 154831600, 3151456000, 71830281600, 1809141934600, 49559087177600, 1459865188782000, 45970426027926400, 1543274016213529600, 55120521154277779200, 2088917638216953544000, 83717918489664018560000
OFFSET
0,3
FORMULA
a(n) = (n!/(n+1)) * Sum_{k=0..floor(n/3)} (n-3*k)^k * binomial(n+1,n-3*k)/(6^k * k!).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1+x*exp(x^3/6)))/x))
(PARI) a(n) = n!*sum(k=0, n\3, (n-3*k)^k*binomial(n+1, n-3*k)/(6^k*k!))/(n+1);
CROSSREFS
Cf. A365287.
Sequence in context: A006117 A118025 A226773 * A119966 A256599 A377132
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 05 2024
STATUS
approved