A054460 A001333(n), n >= 1, convolved twice with itself.

1, 9, 48, 204, 765, 2649, 8680, 27312, 83313, 247985, 723624, 2077164, 5880797, 16454865, 45577200, 125130432, 340882113, 922265721, 2479938368, 6631802220, 17646603933, 46744464745, 123314065944, 324085913136, 848801213425

Offset: 0

Author

Wolfdieter Lang, Apr 26 2000

Keywords

• easy
• nonn

Comments

a(n) = A054458(n+2,2) (third column of convolution triangle).

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-9,-4,9,6,1)

Crossrefs

Cf. A054458, A054459, A001333, A002203.

Programs

Mathematica

LinearRecurrence[{6, -9, -4, 9, 6, 1}, {1, 9, 48, 204, 765, 2649}, 30] (* Paolo Xausa, Feb 06 2024 *)

Formula

a(n) = (n+1)*(LP2(n+1)+2*LP2(n)+LP2(n-1))/8, n >= 1, LP2(n) = A054459(n), a(0) = 1.

a(n) = (n+1)*((10*n+11)*LP(n)+(4*n+5)*LP(n-1))/16, n >= 1, LP(n) = A001333(n+1).

G.f.: ((1+x)/(1-2*x-x^2))^3.

a(n) = +6*a(n-1) -9*a(n-2) -4*a(n-3) +9*a(n-4) +6*a(n-5) +a(n-6). - R. J. Mathar, Feb 05 2024