A370282 Coefficient of x^n in the expansion of 1/( (1-x)^3 - x )^n.

1, 4, 42, 499, 6250, 80634, 1060269, 14127852, 190102482, 2577310285, 35150819132, 481734467955, 6628611532621, 91517611501008, 1267182734325900, 17589579427715124, 244689432718144770, 3410399867585709501, 47613678409439712861, 665756829352248572725

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(4*n+2*k-1,n-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) ). See A369215.

Prog

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

Crossrefs

Cf. A069723, A370280.

Cf. A369215.

Sequence in context: A335776 A388422 A092800 * A268542 A249928 A156440

Adjacent sequences: A370279 A370280 A370281 * A370283 A370284 A370285

Keyword

nonn

Author

Seiichi Manyama, Feb 13 2024

Status

approved