A292476 Number of solutions to +-1 +- 3 +- 5 +- 7 +- ... +- (4*n-1) = 0.

1, 0, 2, 2, 8, 20, 68, 206, 692, 2306, 7930, 27492, 96792, 343670, 1231932, 4447510, 16164914, 59086618, 217091832, 801247614, 2969432270, 11045446688, 41224168020, 154329373022, 579377940390, 2180684278698, 8227240466520, 31107755899600

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Formula

Constant term in the expansion of Product_{k=1..2*n} (x^(2*k-1)+1/x^(2*k-1)).

a(n) = 2*A156700(n) for n > 0.

Example

For n=2 the 2 solutions are +1-3-5+7 = 0 and -1+3+5-7 = 0.
For n=3 the 2 solutions are +1+3+5-7+9-11 = 0 and -1-3-5+7-9+11 = 0.

Mathematica

a[n_] := SeriesCoefficient[Product[x^(2k - 1) + 1/x^(2k - 1), {k, 1, 2n}], {x, 0, 0}];
Table[a[n], {n, 0, 27}] (* Jean-François Alcover, Mar 10 2023 *)

Prog

(PARI) {a(n) = polcoeff(prod(k=1, 2*n, x^(2*k-1)+1/x^(2*k-1)), 0)}

Crossrefs

Cf. A063865, A156700, A292496.

Sequence in context: A060823 A330645 A178076 * A348534 A259807 A137774

Adjacent sequences: A292473 A292474 A292475 * A292477 A292478 A292479

Keyword

nonn

Author

Seiichi Manyama, Sep 17 2017

Status

approved