A171531 Irregular triangle read by rows: first row is 1, n-th row (n > 0) consists of the coefficients in the expansion of H(x;n)*(x + 1)^(n - 1)/2^floor(n/2), where H(x;n) is the Hermite polynomial of order n.

1, 0, 2, -1, -1, 2, 2, 0, -6, -12, -2, 8, 4, 3, 9, -3, -33, -32, 0, 12, 4, 0, 30, 120, 140, -40, -202, -128, 8, 32, 8, -15, -75, -60, 300, 765, 585, -142, -470, -220, 20, 40, 8, 0, -210, -1260, -2730, -1680, 2982, 6132, 3586, -744, -1860, -688, 72, 96, 16, 105, 735, 1365

Offset

0,3

Links

Table of n, a(n) for n=0..59.

Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, 2009, page 695.

Example

Triangle begins:
    1;
    0,   2;
   -1,  -1,   2,   2;
    0,  -6, -12,  -2,   8,    4;
    3,   9,  -3, -33, -32,    0,   12,    4;
    0,  30, 120, 140, -40, -202, -128,    8,   32,  8;
  -15, -75, -60, 300, 765,  585, -142, -470, -220, 20, 40, 8;
   ... reformatted. - Franck Maminirina Ramaharo, Oct 02 2018

Mathematica

Join[{1}, Table[CoefficientList[HermiteH[n, x]*(x + 1)^(n - 1)/2^Floor[n/2], x], {n, 1, 12}]]//Flatten

Crossrefs

Cf. A007318, A060821, A171229, A171631.

Sequence in context: A307014 A240871 A236765 * A171532 A171533 A115236

Adjacent sequences: A171528 A171529 A171530 * A171532 A171533 A171534

Keyword

sign,tabf

Author

Roger L. Bagula, Dec 11 2009

Extensions

Edited and new name by Franck Maminirina Ramaharo, Oct 02 2018

Status

approved