A370283 Coefficient of x^n in the expansion of 1/( (1-x)^3 - x^2 )^n.

1, 3, 23, 201, 1855, 17643, 171059, 1680822, 16679031, 166763190, 1677365833, 16953705860, 172047413395, 1751870166998, 17890003430490, 183148065506136, 1879053717936423, 19315569214866495, 198890064249729314, 2051053032020625350, 21180292180328586305

Offset: 0

Author

Seiichi Manyama, Feb 13 2024

Keywords

• nonn

Links

• a(n) = Sum_{k=0..floor(n/2)} binomial(n+k-1,k) * binomial(4*n+k-1,n-2*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^2) ). See A369694.

Crossrefs

Cf. A370282, A370284.

Cf. A369694.

Programs

PARI

a(n) = sum(k=0, n\2, binomial(n+k-1, k)*binomial(4*n+k-1, n-2*k));