|
| |
|
|
A194938
|
|
Triangle read by rows: coefficients of polynomials p(x,n) defined by 1/(1-t-t^2)^x=Sum_{n=1..oo} p(x,n)*t^n/n!.
|
|
1
|
|
|
|
1, 0, 1, 0, 3, 1, 0, 8, 9, 1, 0, 42, 59, 18, 1, 0, 264, 450, 215, 30, 1, 0, 2160, 4114, 2475, 565, 45, 1, 0, 20880, 43512, 30814, 9345, 1225, 63, 1, 0, 236880, 528492, 420756, 154609, 27720, 2338, 84, 1, 0, 3064320, 7235568, 6316316, 2673972, 594489, 69552
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,5
|
|
|
COMMENTS
|
A039692 is a similar triangle but without the leading column.
1/(1-t-t^2) is the g.f. for the Fibonacci numbers (A000045).
Row sums: A005442(n-1).
|
|
|
REFERENCES
|
Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 149-150
|
|
|
LINKS
|
Table of n, a(n) for n=1..52.
|
|
|
EXAMPLE
|
Triangle begins
1;
0, 1;
0, 3, 1;
0, 8, 9, 1;
0, 42, 59, 18, 1;
0, 264, 450, 215, 30, 1;
0, 2160, 4114, 2475, 565, 45, 1;
0, 20880, 43512, 30814, 9345, 1225, 63, 1;
0, 236880, 528492, 420756, 154609, 27720, 2338, 84, 1;
0, 3064320, 7235568, 6316316, 2673972, 594489, 69552, 4074, 108, 1;
0, 44634240, 110499696, 103889700, 49087520, 12803175, 1887753, 154350, 6630, 135, 1;
|
|
|
MATHEMATICA
|
p[t_] = 1/(1 - t - t^2)^x; Table[ ExpandAll[n!SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[n!* CoefficientList[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]
|
|
|
CROSSREFS
|
Cf. A000045, A005442, A039692
Sequence in context: A052420 A162971 A078521 * A135871 A126178 A094753
Adjacent sequences: A194935 A194936 A194937 * A194939 A194940 A194941
|
|
|
KEYWORD
|
nonn,tabl
|
|
|
AUTHOR
|
Roger L. Bagula, Apr 17 2008
|
|
|
EXTENSIONS
|
Edited by N. J. A. Sloane, Aug 28 2011
|
|
|
STATUS
|
approved
|
| |
|
|
