A392639 Expansion of 1 / ((1-x)^5 - x^5)^2.

1, 10, 55, 220, 715, 2004, 5035, 11680, 25670, 54740, 115637, 245540, 527120, 1141580, 2478135, 5357532, 11489175, 24414650, 51475350, 107942700, 225697580, 471409650, 984407325, 2055138800, 4287086100, 8930208942, 18567332720, 38527680460, 79799428840, 165031628730

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,254,-220,140,-65,20,-4).

Formula

G.f.: B(x)^2, where B(x) is the g.f. of A049016.

a(n) = Sum_{k=0..floor(n/5)} (k+1) * binomial(n+9,n-5*k).

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 254*a(n-5) - 220*a(n-6) + 140*a(n-7) - 65*a(n-8) + 20*a(n-9) - 4*a(n-10).

Mathematica

Table[Sum[(k+1)*Binomial[n+9, n-5*k], {k, 0, Floor[n/5]}], {n, 0, 35}] (* Vincenzo Librandi, Jan 19 2026 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/((1-x)^5-x^5)^2)
(Magma) R<x>:=PowerSeriesRing(Rationals(), 35); Coefficients(R! 1 / ((1-x)^5 - x^5)^2); // Vincenzo Librandi, Jan 19 2026

Crossrefs

Cf. A392580, A392583, A392586, A392589.

Cf. A049016.

Sequence in context: A243744 A145459 A290893 * A392589 A392586 A034241

Adjacent sequences: A392636 A392637 A392638 * A392640 A392641 A392642

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 18 2026

Status

approved