A368079 Expansion of (1/x) * Series_Reversion( x * (1-x)^3 * (1-x^2)^3 ).

1, 3, 18, 127, 996, 8322, 72644, 654615, 6043455, 56866028, 543368586, 5258196762, 51426990112, 507537393600, 5048033356128, 50549237164615, 509197913456922, 5156339940802941, 52460340305220466, 535976129228082972, 5496745175387480976

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..963

Index entries for reversions of series

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(3*n+k+2,k) * binomial(4*n-2*k+2,n-2*k).

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

a(n) = (1/(n+1)) * [x^n] 1/( (1+x)^3 * (1-x)^6 )^(n+1). - Seiichi Manyama, Feb 16 2024

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^3*(1-x^2)^3)/x)
(PARI) a(n, s=2, t=3, u=3) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);

Crossrefs

Cf. A365752, A365856.

Cf. A365878, A365879.

Cf. A130565, A369301.

Cf. A369264, A370271.

Sequence in context: A264230 A377106 A369264 * A373313 A120922 A360446

Adjacent sequences: A368076 A368077 A368078 * A368080 A368081 A368082

Keyword

nonn

Author

Seiichi Manyama, Jan 18 2024

Status

approved