A396724 a(n) = (-4^n/2) p(n, -3/2), where p(n,x) is the Lagrange interpolating polynomial through (1,0) and (k,1) for k=2..n+1.

0, 5, 55, 430, 2875, 17506, 100054, 546076, 2877139, 14741786, 73840002, 362963908, 1756073182, 8381571028, 39537088012, 184595889208, 854091531907, 3920036136778, 17862714586762, 80870371149748, 363985389650602, 1629529723109308, 7259813777148532

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

Conjecture D-finite with recurrence n*a(n) +2*(-4*n-3)*a(n-1) +8*(2*n+3)*a(n-2)=0. - R. J. Mathar, Jun 30 2026

Mathematica

t[0] = {0}; t[n_] := t[n] = Join[t[n - 1], {1}];
p[n_, x_] := Expand[InterpolatingPolynomial[t[n], x]];
Table[(-4^n/2) p[n, -3/2], {n, 0, 40}]
Labeled[Plot[{p[1, x], p[2, x], p[3, x], p[4, x], p[5, x]}, {x, -1, 7}], "Plot of p[n, x] for n=1..5."]

Crossrefs

Cf. A395640, A004442, A125577, A000531, A000346, A396722, A396723.

Sequence in context: A015266 A138163 A335355 * A306095 A081300 A190543

Adjacent sequences: A396721 A396722 A396723 * A396725 A396726 A396727

Keyword

nonn,changed

Author

Clark Kimberling, Jun 20 2026

Status

approved