A111882 Row sums of triangle A111595 (normalized rescaled squared Hermite polynomials).

1, 1, 0, 4, 4, 36, 256, 400, 17424, 784, 1478656, 876096, 154753600, 560363584, 19057250304, 220388935936, 2564046397696, 83038749753600, 327933273309184, 33173161139160064, 26222822450021376, 14475245839622726656

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..449

Formula

E.g.f.: exp(x/(1+x))/sqrt(1-x^2).

a(n) = Sum_{m=0..n} A111595(n, m), n>=0.

A111882(n) = A001464(n)^2. - Mark van Hoeij, Nov 11 2009

Conjecture: a(n) +(n-2)*a(n-1) -(n-1)*(n-2)*a(n-2) -(n-1)*(n-2)^2*a(n-3)=0. - R. J. Mathar, Oct 05 2014

Mathematica

With[{nmax = 50}, CoefficientList[Series[Exp[x/(1 + x)]/Sqrt[1 - x^2], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jun 10 2018 *)

Prog

(Python)
from sympy import hermite, Poly, sqrt
def a(n): return sum(Poly(1/2**n*hermite(n, sqrt(x/2))**2, x).all_coeffs()) # Indranil Ghosh, May 26 2017
(PARI) x='x+O('x^30); Vec(serlaplace(exp(x/(1+x))/sqrt(1-x^2))) \\ G. C. Greubel, Jun 10 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(x/(1+x))/Sqrt(1-x^2))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jun 10 2018

Crossrefs

Cf. A111883 (unsigned row sums of A111595).

Sequence in context: A129357 A100303 A192348 * A321313 A070959 A367643

Adjacent sequences: A111879 A111880 A111881 * A111883 A111884 A111885

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 23 2005

Status

approved