A111777 Fourth column (m=3) of unsigned triangle A111595.

1, 12, 130, 1380, 15435, 182280, 2302020, 30958200, 444230325, 6771510900, 109568809350, 1874844071100, 33875023557375, 644264598978000, 12877256933541000, 269789087886318000, 5915648230774907625, 135459771081512377500, 3234745039813583546250

Offset: 3

Author

Wolfdieter Lang, Aug 23 2005

Keywords

• nonn
• easy

Crossrefs

Cf. A111595.

Programs

PARI

a(n) = {my(p = polhermite(n)^2/2^n); my(q = sum(k=1, poldegree(p), polcoef(p, k)/2^(k/2)*x^k)); abs(polcoef(q, 6));} \\ Michel Marcus, Jan 06 2021

Formula

E.g.f.: (1/sqrt(1-x^2))*((x/(1-x))^3)/3!.

a(n) = (n!/3!) * Sum_{k=0..floor((n-3)/2)} binomial(2*k, k)*binomial(n-2*k-1, 2)/(4^k), n >= 3.

D-finite with recurrence (-n+3)*a(n) +3*n*a(n-1) +n*(n-1)^2*a(n-2)=0. - R. J. Mathar, Aug 11 2025