A055994 Expansion of (1+6x)/(1-x)^10.

1, 16, 115, 550, 2035, 6292, 17017, 41470, 92950, 194480, 384098, 722228, 1301690, 2261000, 3801710, 6210644, 9887999, 15382400, 23434125, 35027850, 51456405, 74397180, 106002975, 149009250, 206859900, 283853856, 385314996, 517788040

Offset: 0

Author

Barry E. Williams, Jun 04 2000

Keywords

• easy
• nonn

Comments

Partial sums of A034266. - Vladimir Joseph Stephan Orlovsky, Jun 25 2009

References

• A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1)

Crossrefs

Cf. A034266.

Cf. A093564 ((7, 1) Pascal, column m=9). Partial sums of A034266.

Programs

Magma

[((7*n+9)*Binomial(n+8,8))/9: n in [0..40]]; // Vincenzo Librandi, Jul 30 2014

Mathematica

CoefficientList[Series[(1 + 6 x)/(1 - x)^10, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 30 2014 *)
LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1,16,115,550,2035,6292,17017,41470,92950,194480},30] (* Harvey P. Dale, Sep 07 2022 *)

Formula

a(n) = (7n+9)*C(n+8, 8)/9.

G.f.: (1+6x)/(1-x)^10.