|
Search: id:A103519
|
|
|
| A103519 |
|
a(1) = 1, a(n) = sum of n successive numbers starting with a(n-1) + 1. |
|
+0
2
|
|
| 1, 5, 21, 94, 485, 2931, 20545, 164396, 1479609, 14796145, 162757661, 1953092010, 25390196221, 355462747199, 5331941208105, 85311059329816, 1450288008607025, 26105184154926621, 495998498943605989, 9919969978872119990
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
FORMULA
|
a(n+1) = k(k+1)/2 - a(n)*(a(n)+1)/2, where k = a(n) + n +1.
a(n) = Sum[i=0..n] n!/(n-i)! * (n-i)(n-i+1)/2 = Sum[i=0..n] n!/(n-i)! * A000217(n-i). For n>2, a(n) = 3*n*(n-1)/2*floor((n-2)!*e)+n, where e=exp(1). - Max Alekseyev (maxal(AT)cs.ucsd.edu), Feb 14 2005
a(n) = n*a(n-1) + n(n+1)/2. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 16 2008
|
|
EXAMPLE
|
a(2) = 2+3 = 5, a(3) = 6+7+8 = 21, a(4) = 22 +23 +24 +25.
|
|
MAPLE
|
a[1]:=1: for n from 2 to 20 do a[n]:=n*a[n-1]+(1/2)*n*(n+1) end do: seq(a[n], n=1..20); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 16 2008
|
|
PROGRAM
|
(PARI) { t(n) = n*(n+1)/2 } { a(n) = sum(i=0, n, n!/(n-i)!*t(n-i)) } { a2(n) = 3*t(n-1)*floor((n-2)!*exp(1))+n } (Alekseyev)
|
|
CROSSREFS
|
Cf. A103520.
Sequence in context: A007287 A116904 A126952 this_sequence A017968 A017969 A050897
Adjacent sequences: A103516 A103517 A103518 this_sequence A103520 A103521 A103522
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 10 2005
|
|
EXTENSIONS
|
More terms from Max Alekseyev (maxal(AT)cs.ucsd.edu), Feb 14 2005
|
|
|
Search completed in 0.002 seconds
|
