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A358688
a(n) = n! * Sum_{k=0..n} k^(k * (n-k)) / (n-k)!.
2
1, 2, 5, 34, 869, 75866, 28213327, 39049033346, 256215628707257, 7710689746589777938, 1063776147486867074877851, 870059224717752809087935599002, 3104894940194751778363241199111802885, 77521065749331962430758061530260243383954602
OFFSET
0,2
LINKS
FORMULA
E.g.f.: Sum_{k>=0} x^k * exp(k^k * x).
G.f.: Sum_{k>=0} k! * x^k / (1 - k^k * x)^(k+1).
MATHEMATICA
Table[1 + n!*Sum[k^(k*(n-k))/(n-k)!, {k, 1, n}], {n, 0, 12}] (* Vaclav Kotesovec, Nov 27 2022 *)
PROG
(PARI) a(n) = n!*sum(k=0, n, k^(k*(n-k))/(n-k)!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k*exp(x)^k^k)))
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, k!*x^k/(1-k^k*x)^(k+1)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 26 2022
STATUS
approved