A329968
a(0) = 1; a(n) = Sum_{k=1..n} |Stirling1(n,k)| * a(n-k).
Original entry on oeis.org
1, 1, 2, 8, 77, 2329, 302564, 222085736, 1123297137786, 45315713537365706, 16445319538981321524068, 59677257201788875416461684008, 2382127122661172512076372104185900762, 1141042791864963721866517729601372480006639394, 7105297245805890887235402087045369387823693986873653108
Offset: 0
-
a:= proc(n) option remember; `if`(n=0, 1,
add(a(n-j)*abs(Stirling1(n, j)), j=1..n))
end:
seq(a(n), n=0..14); # Alois P. Heinz, Feb 25 2025
-
a[n_] := a[n] = Sum[Abs[StirlingS1[n, k]] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 13}]
A329967
a(0) = 1; a(n) = Sum_{k=1..n} Stirling1(n,k) * a(n-k).
Original entry on oeis.org
1, 1, 0, -2, 7, 259, -28726, -21126778, 106100219840, 4280272610298752, -1553116380131413822408, -5635994212344216419883091608, 224970666556043231138664445792724812, 107761317610991666102026987955237496031475980
Offset: 0
-
a[n_] := a[n] = Sum[StirlingS1[n, k] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 13}]
A381515
a(n) = Sum_{j=1..n} Stirling2(n-1,j-1) * a(n-j) for n>=1, starting with a(0) = 1.
Original entry on oeis.org
1, 1, 1, 2, 5, 16, 71, 432, 3446, 35805, 493247, 9055817, 219034736, 6924788187, 287364757172, 15747872749912, 1138063678023858, 107917571120653077, 13417659577126888599, 2194989270698166806727, 473329783091262653789042, 134287984058139116699933228
Offset: 0
-
a:= proc(n) option remember; `if`(n=0, 1,
add(a(n-j)*Stirling2(n-1, j-1), j=1..n))
end:
seq(a(n), n=0..23);
Showing 1-3 of 3 results.