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A293847
E.g.f.: exp(Sum_{n>=1} n!*x^n).
3
1, 1, 5, 49, 793, 19361, 672061, 31721425, 1963804529, 154746407233, 15136503333301, 1799712380844401, 255578390749947145, 42713809784784354529, 8296411053128532892013, 1852797862395580239567121, 471358206112272764630500321, 135500644700064476406317390465
OFFSET
0,3
LINKS
FORMULA
a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..n} k*k!*a(n-k)/(n-k)! for n > 0.
a(n) ~ n!^2. - Vaclav Kotesovec, Oct 18 2017
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(
a(n-i)*binomial(n-1, i-1)*i!^2, i=1..n))
end:
seq(a(n), n=0..20); # Alois P. Heinz, Dec 02 2021
MATHEMATICA
nmax = 20; CoefficientList[Series[E^Sum[k!*x^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 18 2017 *)
PROG
(PARI) {a(n) = n!*polcoeff(exp(sum(k=1, n, k!*x^k)+x*O(x^n)), n)}
CROSSREFS
Sequence in context: A357335 A290755 A062995 * A104600 A221972 A002111
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 17 2017
STATUS
approved