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A343900
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a(n) = Sum_{k=0..n} (k!)^(k+1) * binomial(n,k).
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4
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1, 2, 11, 1324, 7967861, 2986023826166, 100306147958903465407, 416336313421816733159702737376, 281633758448076539969292901914477101456489, 39594086612245054028213574779019294652734771094507399786
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OFFSET
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0,2
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COMMENTS
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Binomial transform of (n!)^(n+1).
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LINKS
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FORMULA
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G.f.: Sum_{k>=0} (k!)^(k+1) * x^k/(1 - x)^(k+1).
E.g.f.: exp(x) * Sum_{k>=0} (k! * x)^k.
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MATHEMATICA
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a[n_] := Sum[(k!)^(k+1) * Binomial[n, k], {k, 0, n}]; Array[a, 10, 0] (* Amiram Eldar, May 05 2021 *)
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PROG
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(PARI) a(n) = sum(k=0, n, k!^(k+1)*binomial(n, k));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, k!^(k+1)*x^k/(1-x)^(k+1)))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x)*sum(k=0, N, (k!*x)^k)))
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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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