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A376094
E.g.f. A(x) satisfies A(x) = x * exp(3*A(x)) * (1 + A(x)).
2
0, 1, 8, 141, 3912, 148845, 7210368, 424596753, 29451533184, 2352033716409, 212561497036800, 21446708257599669, 2389752470910624768, 291465187429985987301, 38621040916534872219648, 5524829459141297215253625, 848620611495100582915571712
OFFSET
0,3
FORMULA
E.g.f.: Series_Reversion( x * exp(-3*x) / (1 + x) ).
a(n) = n! * Sum_{k=1..n} (3*n)^(k-1) * binomial(n-1,k-1)/k!.
a(n) ~ ((5 + sqrt(21))/2)^n * n^(n-1) / (3^(3/4) * 7^(1/4) * exp((5 - sqrt(21))*n/2)). - Vaclav Kotesovec, Sep 10 2024
PROG
(PARI) a(n) = n!*sum(k=1, n, (3*n)^(k-1)*binomial(n-1, k-1)/k!);
CROSSREFS
Sequence in context: A224735 A090931 A367199 * A239757 A295242 A305763
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 10 2024
STATUS
approved