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

3,2

Links

Table of n, a(n) for n=3..21.

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.

Prog

(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

Crossrefs

Cf. A111595.

Sequence in context: A239407 A360878 A163414 * A209013 A341588 A240798

Adjacent sequences: A111774 A111775 A111776 * A111778 A111779 A111780

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 23 2005

Status

approved