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Putnam
1984 Putnam
B1
B1
Part of
1984 Putnam
Problems
(1)
recursion for 1!+2!+...+n!
Source: Putnam 1984 B1
9/2/2021
Let
n
n
n
be a positive integer, and define
f
(
n
)
=
1
!
+
2
!
+
…
+
n
!
f(n)=1!+2!+\ldots+n!
f
(
n
)
=
1
!
+
2
!
+
…
+
n
!
. Find polynomials
P
P
P
and
Q
Q
Q
such that
f
(
n
+
2
)
=
P
(
n
)
f
(
n
+
1
)
+
Q
(
n
)
f
(
n
)
f(n+2)=P(n)f(n+1)+Q(n)f(n)
f
(
n
+
2
)
=
P
(
n
)
f
(
n
+
1
)
+
Q
(
n
)
f
(
n
)
for all
n
≥
1
n\ge1
n
≥
1
.
number theory
Sequences
recurrence relation