|
| |
|
|
A131927
|
|
Series reversion of x * (1 - 9*x) / (1 - x).
|
|
2
| |
|
|
0, 1, 8, 136, 2888, 68680, 1749896, 46707976, 1289214152, 36496595656, 1053849164552, 30918300671368, 919029058099784, 27617782977715528, 837674888992142984, 25610757376777402888, 788450850824647610312
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| The Hankel transform of this sequence is 72^C(n+1,2) .
|
|
|
FORMULA
| a(n) = Sum_{k, 0<=k<=n} A086810(n,k)*8^k .
G.f.: (1+x-sqrt(1-34*x+x^2))/18. - Emeric Deutsch, Nov 19 2007
a(n) = - a(n-1) + 9 * Sum_{k=1..n-1} a(k) * a(n-k) if n>1. - Michael Somos, Jul 23 2011
|
|
|
EXAMPLE
| x + 8*x^2 + 136*x^3 + 2888*x^4 + 68680*x^5 + 1749896*x^6 + 46707976*x^7 + ...
|
|
|
MAPLE
| G:=(1+x-sqrt(1-34*x+x^2))*1/18: Gser:=series(G, x=0, 21): seq(coeff(Gser, x, n), n =0..17); - Emeric Deutsch, Nov 19 2007
|
|
|
PROG
| (PARI) {a(n) = local(A); if( n<1, 0, A = vector(n); A[1] = 1; for( k=2, n, A[k] = - A[k-1] + 9 * sum( j=1, k-1, A[j] * A[k-j])); A[n])} /* Michael Somos, Jul 23 2011 */
|
|
|
CROSSREFS
| Sequence in context: A069988 A072072 A195614 * A132869 A036915 A049211
Adjacent sequences: A131924 A131925 A131926 * A131928 A131929 A131930
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 29 2007
|
|
|
EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 19 2007
|
| |
|
|
