A224514 Expansion of (1-x)*(1-3*x)*(1-3*x+x^2)/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).

1, 2, 6, 20, 70, 251, 911, 3327, 12190, 44744, 164407, 604487, 2223504, 8181175, 30108147, 110820165, 407946421, 1501844193, 5529362694, 20358557249, 74961030414, 276017648570, 1016360893036, 3742540945813, 13781324308298, 50748099850042

Offset: 0

Author

Philippe Deléham, Apr 08 2013

Keywords

• nonn
• easy

Comments

A diagonal of the square array A223968.

Links

• Index entries for linear recurrences with constant coefficients, signature (9,-28,35,-15,1).

Crossrefs

Cf. A223968

Programs

Mathematica

LinearRecurrence[{9,-28,35,-15,1},{1,2,6,20,70,251,911,3327,12190,44744,164407,604487,2223504,8181175},40] (* Harvey P. Dale, Apr 24 2016 *)

Formula

a(n) = A223968(n,n).

G.f.: (1-x)*(1-3*x)*(1-3*x+x^2)/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).

a(n) = 9*a(n-1) - 28*a(n-2) + 35*a(n-3) - 15*a(n-4) + a(n-5) with a(0) = 1, a(1) = 2, a(2) = 6, a(3) = 20, a(4) = 70.

Extensions

a(8) corrected by Georg Fischer, May 10 2019