|
Search: id:A098432
|
|
|
| A098432 |
|
Coefficients of polynomials S(n,x) related to Springer numbers. |
|
+0
4
|
|
| 1, 8, 7, 128, 304, 177, 3072, 13952, 21080, 10199, 98304, 724992, 2016000, 2441056, 1051745, 3932160, 42762240, 187643904, 407505664, 428605352, 169913511, 188743680, 2839019520, 17974591488, 60428242944, 111985428352
(list; table; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
A. Randrianarivony and J. Zeng, Une famille des polynomes qui interpole plusieurs suites..., Adv. Appl. Math. 17 (1996), 1-26.
|
|
FORMULA
|
Recurrence: S(0, x)=1, S(n, x)=(2x+2)(2x+4)S(n-1, x+2)-(2x+1)^2S(n-1, x).
G.f.: Sum[n>=0, S(n, x)t^n] = 1/(1+t-4*2(x+1)t/(1-4*2(x+2)t/(1+t-4*4(x+3)t/(1-4+4(x+4)t/...)))).
|
|
EXAMPLE
|
S(0,x) = 1,
S(1,x) = 8*x + 7,
S(2,x) = 128*x^2 + 304*x + 177,
S(3,x) = 3072*x^3 + 13952*x^2 + 21080*x + 10199.
|
|
PROGRAM
|
(PARI) S(n, x)=if(n<1, 1, (2*x+2)*(2*x+4)*S(n-1, x+2)-(2*x+1)^2*S(n-1, x))
|
|
CROSSREFS
|
Cf. A001586. S(n, 1/2) = A000464(n+1), S(n, -1/2) = A000281(n).
Leading coefficients are A051189. Constant terms are in A098433.
Cf. A001586. S(n, 1/2) = A000464(n), S(n, -1/2) = A000281(n).
Sequence in context: A090099 A138809 A038285 this_sequence A127583 A113809 A019960
Adjacent sequences: A098429 A098430 A098431 this_sequence A098433 A098434 A098435
|
|
KEYWORD
|
tabl,nonn
|
|
AUTHOR
|
Ralf Stephan, Sep 07 2004
|
|
|
Search completed in 0.002 seconds
|
