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A390409
a(n) = Sum_{k=0..n} binomial(4*n+3*k,n-k).
4
1, 5, 40, 344, 3046, 27398, 248857, 2275452, 20906144, 192779081, 1782715547, 16523337885, 153436815280, 1427064778720, 13290364757887, 123916149226892, 1156515716165621, 10803258048628500, 100993587926942929, 944783278987891098, 8843805326964655887
OFFSET
0,2
LINKS
FORMULA
G.f.: 1/((1-4*x*g^3) * (1-x*g^7)) where g = 1+x*g^4 is the g.f. of A002293.
MATHEMATICA
Table[Sum[Binomial[4*n+3*k, n-k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Nov 07 2025 *)
PROG
(PARI) a(n) = sum(k=0, n, binomial(4*n+3*k, n-k));
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 04 2025
STATUS
approved