A064305 Ninth diagonal of triangle A064094.

1, 1430, 95235, 1338790, 9137549, 41260086, 142648495, 409186310, 1022586105, 2298558934, 4750427771, 9170347110, 16730290885, 29104970870, 48618847719, 78419396806, 122678791025, 186826162710

Offset: 0

Author

Wolfdieter Lang, Sep 13 2001

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A009766, A064094, A064304 (eighth diagonal).

Programs

Mathematica

CoefficientList[Series[(1 + 1422 x + 83823 x^2 + 616894 x^3 + 1013799 x^4 + 412698 x^5 + 33337 x^6 + 186 x^7)/(1 - x)^8, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 15 2014 *)

Formula

a(n) = 1 + 7*n + 27*n^2 + 75*n^3 + 165*n^4 + 297*n^5 + 429*n^6 + 429*n^7, compare to row n = 7 of Catalan triangle A009766.

G.f.: (1 + 1422*x + 83823*x^2 + 616894*x^3 + 1013799*x^4 + 412698*x^5 + 33337*x^6 + 186*x^7)/(1 - x)^8.

E.g.f.: exp(x)*(1 + 1429*x + 46188*x^2 + 176229*x^3 + 181170*x^4 + 66792*x^5 + 9438*x^6 + 429*x^7). - Stefano Spezia, Jul 24 2022