A064304 Eighth diagonal of triangle A064094.

1, 429, 14589, 137089, 702297, 2537781, 7312789, 17981769, 39322929, 78571837, 146150061, 256488849, 428947849, 688828869, 1068484677, 1608522841, 2359104609, 3381338829, 4748770909, 6548966817

Offset: 0

Author

Wolfdieter Lang, Sep 13 2001

Keywords

• nonn
• easy

Links

• Stefano Spezia, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

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

Formula

a(n) = 1 + 6*n + 20*n^2 + 48*n^3 + 90*n^4 + 132*n^5 + 132*n^6, compare to row n = 6 of Catalan triangle A009766.

G.f.: (1 + 422*x + 11607*x^2 + 43940*x^3 + 34063*x^4 + 4950*x^5 + 57*x^6)/(1 - x)^7.

E.g.f.: exp(x)*(1 + 428*x + 6866*x^2 + 15768*x^3 + 9990*x^4 + 2112*x^5 + 132*x^6). - Stefano Spezia, Jul 24 2022