|
Search: id:A128386
|
|
|
| A128386 |
|
Expansion of c(3x^2)/(1-xc(3x^2)), c(x) the g.f. of A000108. |
|
+0
5
|
|
| 1, 1, 4, 7, 28, 58, 232, 523, 2092, 4966, 19864, 48838, 195352, 492724, 1970896, 5068915, 20275660, 52955950, 211823800, 560198962, 2240795848, 5987822380, 23951289520, 64563867454, 258255469816, 701383563388, 2805534253552
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Hankel transform is 3^C(n+1,2)=A047656(n+1). Series reversion of x(1+x)/(1+2x+4x^2).
|
|
FORMULA
|
G.f.: (sqrt(1-12x^2)+2x-1)/(2x(1-4x)); a(n)=(1/(n+1))sum{k=0..n+1, sum{j=0..k, C(n,k)C(k,j)C(2n-2k+j,n-2k+j)(-1)^(n-2k+j)2^j4^(k-j)}}; a(n)=sum{k=0..floor(n/2), C(n,n-k)*(n-2k+1)*3^k/(n-k+1)}; a(n)=sum{k=0..floor(n/2), A009766(n-k,k)*3^k};
a(n)=Sum_{k, 0<=k<=n}3^k*A120730(n,n-k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 03 2007
|
|
CROSSREFS
|
Sequence in context: A076148 A146085 A061668 this_sequence A149074 A149075 A149076
Adjacent sequences: A128383 A128384 A128385 this_sequence A128387 A128388 A128389
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Paul Barry (pbarry(AT)wit.ie), Feb 28 2007
|
|
|
Search completed in 0.002 seconds
|
