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A391128

Expansion of g^2/(1 - x*g^4), where g = 1+x*g^3 is the g.f. of A001764.

1, 3, 14, 74, 415, 2410, 14323, 86543, 529462, 3270870, 20365398, 127621431, 804089754, 5089649619, 32344432715, 206262067698, 1319373693135, 8462456016258, 54410275666109, 350603494887850, 2263667614886126, 14641748601524827, 94861527793237043, 615524947205509594

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = Sum_{k=0..n} (4*k+2) * binomial(3*n+k+2,n-k)/(3*n+k+2).

MATHEMATICA

Table[Sum[(4*k+2)*Binomial[3*n+k+2, n-k]/(3*n+k+2), {k, 0, n}], {n, 0, 30}] (* Vincenzo Librandi, Dec 02 2025 *)

PROG

(PARI) a(n) = sum(k=0, n, (4*k+2)*binomial(3*n+k+2, n-k)/(3*n+k+2));

(Magma) [&+[(4*k+2)*Binomial(3*n+k+2, n-k)/(3*n+k+2): k in [0..n]] : n in [0..40] ]; // Vincenzo Librandi, Dec 02 2025