A081905 -id:A081905 - cp's OEIS frontend

A081904 Second binomial transform of binomial(n+6, 6).

1, 9, 60, 344, 1794, 8754, 40636, 181380, 784251, 3302451, 13598280, 54922860, 218131380, 853586100, 3296508840, 12581531064, 47510175861, 177681098205, 658665849636, 2422018974096, 8840103322374, 32044237392726, 115417729279620, 413255236888476, 1471500113899311

Offset: 0

Paul Barry, Mar 31 2003

Binomial transform of A055853 (without leading 0).

3rd binomial transform of (1,6,15,20,15,6,1,0,0,0,...).

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (21,-189,945,-2835,5103,-5103, 2187).

Cf. A000579, A055853, A081905.

m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-2*x)^6/(1-3*x)^7)); // G. C. Greubel, Oct 18 2018

LinearRecurrence[{21,-189,945,-2835,5103,-5103,2187}, {1,9,60,344,1794, 8754,40636}, 50] (* G. C. Greubel, Oct 18 2018 *)

x='x+O('x^30); Vec((1-2*x)^6/(1-3*x)^7) \\ G. C. Greubel, Oct 18 2018

a(n) = 3^n*(n^6 + 93*n^5 + 3055*n^4 + 44055*n^3 + 282424*n^2 + 720132*n + 524880)/524880.
G.f.: (1 - 2*x)^6/(1 - 3*x)^7.
E.g.f.: (720 + 4320*x + 5400*x^2 + 2400*x^3 + 450*x^4 + 36*x^5 + x^6)*exp(3*x) / 720. - G. C. Greubel, Oct 18 2018

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

Original entry on oeis.org

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

Paul Barry, Mar 31 2003

Binomial transform of A081905.

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

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).

Cf. A000579, A081905.

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

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

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

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

cp's OEIS Frontend

A081904 Second binomial transform of binomial(n+6, 6).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula