|
| |
|
|
A015735
|
|
Row sums of triangle A004747.
|
|
5
| |
|
|
1, 3, 17, 145, 1661, 23931, 415773, 8460257, 197360985, 5192853011, 152137882601, 4911873672113, 173268075672277, 6630323916472075, 273555262963272501, 12105084133976359361, 571897644855277242673
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
LINKS
| W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
|
|
|
FORMULA
| E.g.f. exp(1-(1-3*x)^(1/3))-1.
a(n)= 6*(n-2)*a(n-1)-(3*n-8)*(3*n-7)*a(n-2)+a(n-3), a(0) := 1, a(1)=1, a(2)=3.
a(n)=(n-1)!*sum(sum(binomial(k,n-m-k)*(-1/3)^(n-m-k)*binomial(k+n-1,n-1),k,1,n-m)/(m-1)!,m,1,n)+1, n>1. [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Aug 08 2010]
a(n) = D^n(exp(x)) evaluated at x = 0, where D is the operator 1/(1-x)^2*d/dx. Cf. A001515, A016036 and A028575. - Peter Bala, Nov 25 2011
|
|
|
MAPLE
| a(n):=if n=1 then 1 else (n-1)!*sum(sum(binomial(k, n-m-k)*(-1/3)^(n-m-k)*binomial(k+n-1, n-1), k, 1, n-m)/(m-1)!, m, 1, n)+1; (for Maxima) [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Aug 08 2010]
|
|
|
CROSSREFS
| Cf. A001515.
Sequence in context: A198860 A051442 A162650 * A140983 A138013 A052807
Adjacent sequences: A015732 A015733 A015734 * A015736 A015737 A015738
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
|
| |
|
|
