A081906 Fourth binomial transform of binomial(n+6, 6).

1, 11, 100, 820, 6290, 46006, 324556, 2225060, 14902075, 97873625, 632200000, 4025225000, 25307562500, 157349687500, 968628125000, 5909609375000, 35763408203125, 214838427734375, 1281885742187500, 7601284179687500, 44815856933593750, 262824523925781250, 1533738403320312500

Offset: 0

Author

Paul Barry, Mar 31 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A081905.

5th binomial transform of (1,6,15,20,15,6,1,0,0,0,...).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (35,-525,4375,-21875,65625,-109375,78125).

Crossrefs

Cf. A000579, A081905.

Programs

Magma

m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-4*x)^6/(1-5*x)^7)); // G. C. Greubel, Oct 17 2018

Mathematica

LinearRecurrence[{35, -525, 4375, -21875, 65625, -109375, 78125}, {1, 11, 100, 820, 6290, 46006, 324556}, 50] (* G. C. Greubel, Oct 17 2018 *)

PARI

x='x+O(x^30); Vec((1-4*x)^6/(1-5*x)^7) \\ G. C. Greubel, Oct 17 2018

Formula

a(n) = 5^n*(n^6 + 165*n^5 + 9535*n^4 + 238575*n^3 + 2590024*n^2 + 10661700*n + 11250000)/11250000.

G.f.: (1-4*x)^6/(1-5*x)^7.

E.g.f.: (720 + 4320*x + 5400*x^2 + 2400*x^3 + 450*x^4 + 36*x^5 + x^6)*exp(5*x) / 720. - G. C. Greubel, Oct 17 2018