A098432 Coefficients of polynomials S(n,x) related to Springer numbers.

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

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: A038285 A354546 A261117 * A197623 A291692 A127583

Adjacent sequences: A098429 A098430 A098431 * A098433 A098434 A098435

Keyword

tabl,nonn

Author

Ralf Stephan, Sep 07 2004

Status

approved