A039646 Third column of Jabotinsky-triangle A038455 related to A006963.

1, 18, 335, 7155, 176554, 4985316, 159168428, 5681708100, 224518859136, 9737714177928, 460132506980640, 23537198603711520, 1296157111841533824, 76467514565810332800, 4812260962479036076800, 321826321845522830649600

Offset: 0

Author

Wolfdieter Lang

Keywords

• nonn

Comments

Explicit formula for a(n-3) using partitions of n into 3 parts: cf. Knuth's paper for f(n,3) n >= 3, formula with f(k) := A006963(k+1) = (2*k-1)!/k!, k >= 1.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..362
• D. E. Knuth, Convolution polynomials, arXiv:math/9207221 [math.CA], 1992; Mathematica J. 2.1 (1992), no. 4, 67-78.

Crossrefs

Cf. A038455, A006963, A039619.

Programs

Mathematica

Drop[With[{nmax = 20}, CoefficientList[Series[Log[(1 - Sqrt[1 - 4*x])/x/2]^3/6, {x, 0, nmax}], x]*Range[0, nmax]!], 3] (* G. C. Greubel, Dec 14 2017 *)

PARI

my(x='x+O('x^30)); Vec(serlaplace(log((1-sqrt(1-4*x))/x/2)^3/6)) \\ G. C. Greubel, Dec 14 2017

Formula

a(n) = Sum_{j=0..n} binomial(n+2, j)*A006936(j+2)*A039619(n+2-j).

E.g.f.: log((1-sqrt(1-4*x))/x/2)^3/6. - Vladeta Jovovic, May 02 2003