login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A098432 Coefficients of polynomials S(n,x) related to Springer numbers. 3
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; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

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.

PROG

(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: A288188 A038285 A261117 * A197623 A291692 A127583

Adjacent sequences:  A098429 A098430 A098431 * A098433 A098434 A098435

KEYWORD

tabl,nonn

AUTHOR

Ralf Stephan, Sep 07 2004

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 17 15:24 EDT 2019. Contains 324188 sequences. (Running on oeis4.)