A372418 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / (1-x+x^3)^2 ).

1, 0, 0, 2, 2, 2, 15, 32, 53, 192, 527, 1152, 3327, 9578, 24217, 66528, 190357, 515692, 1421172, 4036034, 11272501, 31489762, 89370575, 253106188, 715642419, 2038291672, 5816775442, 16592350656, 47490009821, 136246784272, 391111252072, 1124779108330

Offset

0,4

Links

Table of n, a(n) for n=0..31.

Index entries for reversions of series

Formula

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

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2/(1-x+x^3)^2)/x)
(PARI) a(n, s=3, t=2, u=2) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((u-t+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);

Crossrefs

Cf. A369231, A372416.

Sequence in context: A352029 A025521 A305109 * A068218 A098919 A161748

Adjacent sequences: A372415 A372416 A372417 * A372419 A372420 A372421

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2024

Status

approved