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A355110
Expansion of e.g.f. 2 / (3 - 2*x - exp(2*x)).
6
1, 2, 10, 76, 768, 9696, 146896, 2596448, 52449536, 1191944704, 30097334784, 835973778432, 25330620762112, 831497823494144, 29394162040580096, 1113330929935101952, 44979662118902366208, 1930798895281527717888, 87756941394038739828736, 4210241529540625311727616
OFFSET
0,2
FORMULA
a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} binomial(n,k) * 2^(k-1) * a(n-k).
a(n) ~ n! / ((1 + LambertW(exp(3))) * ((3 - LambertW(exp(3)))/2)^(n+1)). - Vaclav Kotesovec, Jun 19 2022
MATHEMATICA
nmax = 19; CoefficientList[Series[2/(3 - 2 x - Exp[2 x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = n a[n - 1] + Sum[Binomial[n, k] 2^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 19 2022
STATUS
approved