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A143507 Triangle of coefficients of x^n*H_n(x + 1/x), where H_n(x) is the Hermite polynomial of order n. 2
1, 2, 0, 2, 4, 0, 6, 0, 4, 8, 0, 12, 0, 12, 0, 8, 16, 0, 16, 0, 12, 0, 16, 0, 16, 32, 0, 0, 0, -40, 0, -40, 0, 0, 0, 32, 64, 0, -96, 0, -240, 0, -280, 0, -240, 0, -96, 0, 64, 128, 0, -448, 0, -672, 0, -560, 0, -560, 0, -672, 0, -448, 0, 128, 256, 0, -1536, 0, -896, 0, 896, 0, 1680, 0, 896, 0, -896, 0, -1536, 0, 256, 512, 0, -4608, 0, 512 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Row sums yield A144141.
LINKS
FORMULA
E.g.f.: exp(2*(1 + x^2)*y - x^2*y^2). - Franck Maminirina Ramaharo, Oct 25 2018
EXAMPLE
Triangle begins:
1;
2, 0, 2;
4, 0, 6, 0, 4;
8, 0, 12, 0, 12, 0, 8;
16, 0, 16, 0, 12, 0, 16, 0, 16;
32, 0, 0, 0, -40, 0, -40, 0, 0, 0, 32;
64, 0, -96, 0, -240, 0, -280, 0, -240, 0, -96, 0, 64;
128, 0, -448, 0, -672, 0, -560, 0, -560, 0, -672, 0, -448, 0, 128;
... reformatted. - Franck Maminirina Ramaharo, Oct 25 2018
MATHEMATICA
Table[CoefficientList[FullSimplify[x^n*HermiteH[n, x + 1/x]], x], {n,
0, 10}]//Flatten
PROG
(PARI) row(n) = Vec(x^n*subst(polhermite(n, x), x, x+1/x));
for (n=0, 10, print(row(n))); \\ Michel Marcus, Oct 27 2018
CROSSREFS
Cf. A060821.
Sequence in context: A137312 A137320 A263399 * A172040 A317327 A120557
KEYWORD
sign,tabf
AUTHOR
EXTENSIONS
Edited, new name and offset corrected by Franck Maminirina Ramaharo, Oct 25 2018
STATUS
approved

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Last modified May 23 07:28 EDT 2024. Contains 372760 sequences. (Running on oeis4.)