A391779 a(n) = Sum_{k=0..n} 2^k * 3^(n-k) * binomial(k+6,6) * binomial(2*k,2*(n-k)).

1, 14, 154, 2688, 34608, 387744, 4189920, 42410496, 408280992, 3787340480, 33960764992, 295868561408, 2514525570816, 20906787095040, 170489979041280, 1366489403252736, 10783773983748864, 83916508450048512, 644759749272120832, 4896753272486297600, 36796161089297096704

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (28, -280, 1064, -1148, 15008, -124992, 120768, 155568, 5698112, -10145408, -27900544, -137566912, 345705472, 758564864, 2074232832, -4952408832, -6026517504, -13148448768, 44308518912, 7258180608, 33807310848, -209938563072, 151246061568, -69415170048, 386016067584, -609499054080, 365699432448, -78364164096).

Formula

G.f.: (Sum_{k=0..3} 48^k * binomial(7,2*k) * (1-2*x-6*x^2)^(7-2*k) * x^(3*k)) / ((1-2*x-6*x^2)^2 - 48*x^3)^7.

a(n) = 28*a(n-1) - 280*a(n-2) + 1064*a(n-3) - 1148*a(n-4) + 15008*a(n-5) - 124992*a(n-6) + 120768*a(n-7) + 155568*a(n-8) + 5698112*a(n-9) - 10145408*a(n-10) - 27900544*a(n-11) - 137566912*a(n-12) + 345705472*a(n-13) + 758564864*a(n-14) + 2074232832*a(n-15) - 4952408832*a(n-16) - 6026517504*a(n-17) - 13148448768*a(n-18) + 44308518912*a(n-19) + 7258180608*a(n-20) + 33807310848*a(n-21) - 209938563072*a(n-22) + 151246061568*a(n-23) - 69415170048*a(n-24) + 386016067584*a(n-25) - 609499054080*a(n-26) + 365699432448*a(n-27) - 78364164096*a(n-28).

Prog

(PARI) my(A=2, B=3, C=4*A^2*B, N=7, M=30, x='x+O('x^M), X=1-A*x-A*B*x^2, Y=3); Vec(sum(k=0, N\2, C^k*binomial(N, 2*k)*X^(N-2*k)*x^(Y*k))/(X^2-C*x^Y)^N)

Crossrefs

Cf. A108486, A390849.

Cf. A382473, A391723.

Sequence in context: A004986 A154248 A006865 * A263474 A154347 A001707

Adjacent sequences: A391776 A391777 A391778 * A391780 A391781 A391782

Keyword

nonn

Author

Seiichi Manyama, Dec 19 2025

Status

approved