A383379 a(n) = n! * Sum_{k=0..n} (-n)^(n-k) * binomial(n+k,n)/(n-k)!.
1, 1, 4, 21, 176, 1765, 22464, 331177, 5692672, 110286441, 2394828800, 57389046781, 1507401363456, 43018690418509, 1326170009092096, 43905977120300625, 1553942522589937664, 58544111242378404433, 2339326913228257886208, 98816004834223734304741
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, (-n)^(n-k)*binomial(n+k, k)/(n-k)!);
Formula
a(n) = n! * [x^n] exp(-n*x) / (1-x)^(n+1).
a(n) ~ phi^(3*n + 3/2) * n^n / (5^(1/4) * exp(phi*n)), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Apr 25 2025