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

Author

Ralf Stephan, Sep 07 2004

Keywords

• tabl
• nonn

Examples

			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.
		

Links

• A. Randrianarivony and J. Zeng, Une famille des polynomes qui interpole plusieurs suites..., Adv. Appl. Math. 17 (1996), 1-26.

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).

Programs

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))

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/...)))).