A370287 Coefficient of x^n in the expansion of ( (1+x)^3 + x^3 )^n.

1, 3, 15, 87, 531, 3333, 21309, 138015, 902547, 5946153, 39406005, 262404585, 1754316045, 11767931451, 79165530375, 533883963567, 3608242091091, 24432635451465, 165721028062605, 1125743155558677, 7657535953619721, 52151890274636463, 355576809975214095

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

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

The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x / ((1+x)^3 + x^3) ).

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(n, k)*binomial(3*n-3*k, n-3*k));

Crossrefs

Cf. A116411, A370285.

Cf. A188686, A370286.

Cf. A192132.

Sequence in context: A075841 A152596 A278392 * A168503 A370184 A089022

Adjacent sequences: A370284 A370285 A370286 * A370288 A370289 A370290

Keyword

nonn

Author

Seiichi Manyama, Feb 14 2024

Status

approved