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URL: https://oeis.org/A341185

⇱ A341185 - OEIS

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A341185
a(n) = Sum_{k=0..n} k^n * k! * binomial(n,k)^2.
1
1, 1, 12, 315, 15088, 1141625, 124989156, 18659050795, 3638892086208, 897534389449809, 272981684150035300, 100316132701760094251, 43802068733570039425776, 22409162143775383385763913, 13274030650412266312507931652, 9011345457575458529790430999275, 6949138663280794695653315831815936
OFFSET
0,3
FORMULA
a(n) ~ exp(2*sqrt(n/e) - n - 1/e) * n^(2*n) * sqrt(sqrt(e*n)/2) (by saddle-point expansion about k = n - sqrt(n/e)). - Natalia L. Skirrow, Mar 16 2026
MATHEMATICA
a[0] = 1; a[n_] := Sum[k^n * k! * Binomial[n, k]^2, {k, 0, n}]; Array[a, 15, 0] (* Amiram Eldar, Feb 06 2021 *)
PROG
(PARI) a(n) = sum(k=0, n, k^n*k!*binomial(n, k)^2);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 06 2021
EXTENSIONS
More terms from Michel Marcus, Mar 16 2026
STATUS
approved