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A343900
a(n) = Sum_{k=0..n} (k!)^(k+1) * binomial(n,k).
4
1, 2, 11, 1324, 7967861, 2986023826166, 100306147958903465407, 416336313421816733159702737376, 281633758448076539969292901914477101456489, 39594086612245054028213574779019294652734771094507399786
OFFSET
0,2
COMMENTS
Binomial transform of (n!)^(n+1).
LINKS
FORMULA
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.
MATHEMATICA
a[n_] := Sum[(k!)^(k+1) * Binomial[n, k], {k, 0, n}]; Array[a, 10, 0] (* Amiram Eldar, May 05 2021 *)
PROG
(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)))
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 03 2021
STATUS
approved