A392582 Expansion of 1 / ((1-x)^4 - x^2)^2.

1, 8, 38, 144, 489, 1568, 4858, 14696, 43660, 127880, 370330, 1062560, 3025355, 8558080, 24074610, 67398344, 187892467, 521862592, 1444673876, 3987511216, 10976937752, 30145183792, 82605180884, 225908178880, 616686248565, 1680613425240, 4572975709630

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-26,48,-59,48,-26,8,-1).

Formula

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

a(n) = 8*a(n-1) - 26*a(n-2) + 48*a(n-3) - 59*a(n-4) + 48*a(n-5) - 26*a(n-6) + 8*a(n-7) - a(n-8).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/((1-x)^4-x^2)^2)

Crossrefs

Cf. A290890.

Sequence in context: A038732 A038799 A156934 * A036684 A230905 A026640

Adjacent sequences: A392579 A392580 A392581 * A392583 A392584 A392585

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 17 2026

Status

approved