|
| |
|
|
A045994
|
|
a(0)=1, a(n) = M(n) + Sum {M(k)*a(n-k-1), k=1..n-1}, where M(n) are the Motzkin numbers (A001006).
|
|
0
| |
|
|
1, 1, 3, 7, 18, 47, 125, 337, 918, 2522, 6977, 19415, 54297, 152507, 429974, 1216297, 3450817, 9816460, 27991422, 79989880, 229034820, 656979399, 1887653560, 5431969355, 15653355151, 45167783715, 130491471940, 377426429199
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
LINKS
| Vladimir Kruchinin, Compositae and their properties , arXiv:1103.2582
|
|
|
FORMULA
| G.f.: 1/(1-x(1+x)*M(x)), where M(x) is the generating function for the Motzkin numbers. a(n)=sum(sum(k/i*sum(binomial(i,j)*binomial(j,2*j-i-k),j,0,i)*binomial(n-i+k-1,k-1)*(-1)^(n-i),i,k,n),k,1,n), n>0. [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 10 2010]
|
|
|
PROG
| (Other) a(n):=sum(sum(k/i*sum(binomial(i, j)*binomial(j, 2*j-i-k), j, 0, i)*binomial(n-i+k-1, k-1)*(-1)^(n-i), i, k, n), k, 1, n); (for Maxima) [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 10 2010]
|
|
|
CROSSREFS
| Cf. A005773.
Sequence in context: A027969 A027971 A018028 * A101308 A018029 A099483
Adjacent sequences: A045991 A045992 A045993 * A045995 A045996 A045997
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
