A369514 Expansion of (1/x) * Series_Reversion( x * ((1-x)^3-x^3)^2 ).

1, 6, 57, 652, 8250, 111228, 1566384, 22770990, 339136149, 5147965790, 79355002155, 1238845925070, 19546811164017, 311215082863152, 4993737492276384, 80673666233512572, 1311052196736963738, 21418709030787603984, 351563022864652061086, 5794815410347964694408

Offset: 0

Author

Seiichi Manyama, Jan 25 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A369114.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^3-x^3)^2)/x)

PARI

a(n) = sum(k=0, n\3, binomial(2*n+k+1, k)*binomial(7*n+5, n-3*k))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n+k+1,k) * binomial(7*n+5,n-3*k).