|
|
A201952
|
|
A diagonal of irregular triangle A201949.
|
|
3
|
|
|
1, 1, 5, 24, 139, 945, 7377, 65016, 638418, 6910650, 81747665, 1049089470, 14516096009, 215419836359, 3412889885571, 57492203734320, 1026121982213480, 19342642266760680, 383995631680561234, 8007915240045479980, 175020604366224762038, 4000551483475536398178
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
G.f. of row n in triangle A201949 equals Product_{k=0..n-1} (1 + k*x + x^2).
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: Sum_{n>=0} -log(1 - x)^(2*n+1) / (n!*(n+1)!). - Paul D. Hanna, Feb 25 2019
a(n) = [x^(n-1)] Product_{k=0..n-1} (1 + k*x + x^2).
|
|
EXAMPLE
|
E.g.f.: A(x) = x + x^2/2! + 5*x^3/3! + 24*x^4/4! + 139*x^5/5! + 945*x^6/6! + 7377*x^7/7! + 65016*x^8/8! + 638418*x^9/9! + 6910650*x^10/10! + ...
[1],
[(1), 0, 1],
[1,(1), 2, 1, 1],
[1, 3, (5), 6, 5, 3, 1],
[1, 6, 15, (24), 28, 24, 15, 6, 1],
[1, 10, 40, 90,(139), 160, 139, 90, 40, 10, 1], ...
where coefficients in parenthesis form the initial terms of this sequence.
|
|
PROG
|
(PARI) {a(n) = polcoeff( prod(j=0, n-1, 1 + j*x + x^2), n-1)}
for(n=1, 30, print1(a(n), ", "))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Offset changed to 1 to agree with the e.g.f. - Paul D. Hanna, Feb 25 2019
|
|
STATUS
|
approved
|
|
|
|