login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A181990 a(n) = Sum_{0 <= k <= m < p} (binomial(m, k)^(p-1))/p, where p is the n-th prime. 0
3, 399, 12708885, 124515078454872901983423, 39212583445587381894247266262023061, 43487633454143579523135045521112077473364484383507327790688372131, 157851796824901989964381293031623545741924564754192453966085327785455257503133278729 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
a(n) is a sum of all elements in the first p rows of Pascal's triangle each raised to the (p-1) power and divided by p, where p is the n-th prime.
For p = 3 and 7 (and their powers like 3, 9, 27, ... and 7, 49, ...) the sums of all elements in n = p^k top rows of Pascal's triangle each raised to the (n-1) = (p^k-1) power are divisible by n^2 = p^(2k) for all k > 0.
LINKS
Eric Weisstein's World of Mathematics, Pascal's Triangle
Eric Weisstein's World of Mathematics, Binomial Sums
MATHEMATICA
Table[(Sum[Binomial[m, k]^(Prime[n] - 1), {m, 0, Prime[n] - 1}, {k, 0, m}])/Prime[n], {n, 2, 10}]
PROG
(PARI) a(n) = my(p=prime(n)); sum(m=0, p-1, sum(k=0, m, binomial(m, k)^(p-1))/p); \\ Michel Marcus, Dec 03 2018
CROSSREFS
Sequence in context: A199146 A137023 A203563 * A198666 A330014 A305664
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Apr 04 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)