A393908 a(n) = Sum_{i=0..n} Sum_{j=0..i} binomial(n+2*i,3*i) * binomial(i+2*j,3*j).

1, 3, 15, 82, 459, 2589, 14632, 82708, 467399, 2640745, 14917597, 84262525, 475939226, 2688189011, 15183232334, 85756502171, 484361087951, 2735717214249, 15451586796891, 87272004061435, 492920419867581, 2784060522985585, 15724633666463625, 88814198766038561

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (13,-63,154,-215,189,-108,40,-9,1).

Formula

G.f.: ((1-x) * ((1-x)^3 - x))^2 / (((1-x)^3 - x)^3 - x*(1-x)^6).

a(n) = 13*a(n-1) - 63*a(n-2) + 154*a(n-3) - 215*a(n-4) + 189*a(n-5) - 108*a(n-6) + 40*a(n-7) - 9*a(n-8) + a(n-9).

G.f.: 1 / ( (1-x) * (1-B(x)) * (1-B(B(x))) ), where B(x) = x/(1-x)^3.

G.f.: (C(x)/x)^(1/3), where C(x) is the g.f. of A396209.

Prog

(PARI) a(n) = sum(i=0, n, sum(j=0, i, binomial(n+2*i, 3*i)*binomial(i+2*j, 3*j)));

Crossrefs

Cf. A052544, A166482, A396208.

Cf. A396209, A396242.

Sequence in context: A343975 A255676 A015680 * A371516 A084208 A059271

Adjacent sequences: A393905 A393906 A393907 * A393909 A393910 A393911

Keyword

nonn

Author

Seiichi Manyama, May 19 2026

Status

approved