OFFSET
1,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (252, -28116, 1847460, -80186430, 2443408020, -54222394300, 897042522780, -11233051883145, 107495660310160, -790365294823704, 4473663278780448, -19473246213545104, 64926170063690880, -164639495047219200, 314180023114240000, -444424489989120000, 455945899622400000, -328038555648000000, 156378808320000000, -44255232000000000, 5619712000000000).
FORMULA
a(n) = Sum_{j=0..7} (-1)^(j+1)*binomial(3*n+1, 7-j)*(binomial(j+1, 3))^n. - G. C. Greubel, Mar 26 2022
MATHEMATICA
T[n_, k_]:= T[n, k]= Sum[(-1)^(k-j)*Binomial[3*n+1, k-j+2]*(Binomial[j+1, 3])^n, {j, 0, k+2}];
Table[T[n, 5], {n, 30}] (* G. C. Greubel, Mar 26 2022 *)
PROG
(Sage)
@CachedFunction
def T(n, k): return sum( (-1)^(k-j)*binomial(3*n+1, k-j+2)*(binomial(j+1, 3))^n for j in (0..k+2) )
[T(n, 5) for n in (1..30)] # G. C. Greubel, Mar 26 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 29 2009
EXTENSIONS
Terms a(9) and beyond from Andrew Howroyd, May 06 2020
STATUS
approved