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A363010
a(n) = n! * [x^n] 1/(1 - f^n(x)), where f(x) = exp(x) - 1.
2
1, 1, 4, 36, 594, 15775, 618838, 33757864, 2448904188, 228290728635, 26617527649365, 3797508644987398, 651082351708066303, 132130157056046918808, 31333332827346731906130, 8587011712002719806274022, 2693586800519167315881703732, 958983405298849163873718493941
OFFSET
0,3
LINKS
FORMULA
a(n) = T(n,n), T(n,k) = Sum_{j=0..n} Stirling2(n,j) * T(j,k-1), k>1, T(n,0) = n!.
MAPLE
b:= proc(n, t, m) option remember; `if`(n=0, `if`(t<2, m!,
b(m, t-1, 0)), m*b(n-1, t, m)+b(n-1, t, m+1))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..20); # Alois P. Heinz, May 12 2023
CROSSREFS
Main diagonal of A363007.
Main diagonal of A153278 (for n>=1).
Sequence in context: A346292 A086879 A372241 * A263445 A241029 A002761
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 12 2023
STATUS
approved