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A349639
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a(n) = Sum_{k=0..n} binomial(n,k) * A000108(k) * k^k.
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1
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1, 2, 11, 163, 4177, 150606, 7002679, 399296682, 26997867705, 2112814307980, 187919721166951, 18727570061711897, 2067435790679136937, 250474099952311886236, 33043529154916822685459, 4715582224589290429430011, 723854564711343436767660481, 118933484485939500023357177356
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ c * 2^(2*n) * n^(n - 3/2) /sqrt(Pi), where c = Sum_{k>=0} 1/(4^k*k!*exp(k)) = exp(exp(-1)/4) = 1.09633177846412646399584148732...
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MATHEMATICA
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Table[1+Sum[Binomial[n, j]*CatalanNumber[j]*j^j, {j, 1, n}], {n, 0, 20}]
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PROG
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(PARI) a(n) = sum(k=0, n, binomial(n, k) * (binomial(2*k, k)/(k+1)) * k^k); \\ Michel Marcus, Nov 23 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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