A001664 -id:A001664 - cp's OEIS frontend

A001663 Linear coefficient of the n-th converging polynomial of Weber functions (Erroneous version).

Original entry on oeis.org

1, -3, 7, -5, -93, 637, -1425, -22341

Offset: 1

N. J. A. Sloane

sign

The term -93 is a typo in Wynn's table VII and should read -83, see A380170. - R. J. Mathar, Jan 13 2025

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

P. Wynn, Converging factors for the Weber parabolic cylinder functions of complex argument, part Ia, part Ib, Proc. Konin. Ned. Akad. Weten., Series A, 66 (1963), 721-754, Table VII (two parts).
P. Wynn, Converging factors for the Weber parabolic cylinder functions ... [Annotated scan of part 2 only]

Cf. A001664, A001662 (absolute coefficient), A380170 (correct terms).

A380170 Coefficient [k^1] of Wynn's converging polynomial p_n(k) of Weber functions.

Original entry on oeis.org

1, -3, 7, -5, -83, 637, -1425, -22341, 318149, -1415491, -18988393, 444896699, -3268880739, -35114352579, 1317630731647, -14445395761157, -112227733823435, 7047241310852605, -108366459009937881, -487554173851570053, 61301180146129065101, -1271086841777475748099, -1158631507880606959729

Offset: 1

R. J. Mathar, Jan 14 2025

sign

Corrects a typo (-93) in the version published in 1963, A001663.

P. Wynn, Converging factors for the Weber parabolic cylinder functions of complex argument, part Ia, part Ib, Proc. Konin. Ned. Akad. Weten., Series A, 66 (1963), 721-754, Table VII in the 2nd part.

Cf. A380169, A001663.

#re-using code of A001664
seq( p(r,1),r=0..12) ;

a(n) = A380169(n,1).

A380169 Table T(r,s) read by rows: the coefficient of [k^s] of the Wynn's r-th converging polynomial p_r(k) of Weber functions, 0<=s<=r.

Original entry on oeis.org

1, -1, 1, 1, -3, 1, 1, 7, -6, 1, -13, -5, 25, -10, 1, 47, -83, -60, 65, -15, 1, 73, 637, -203, -280, 140, -21, 1, -2447, -1425, 3710, 77, -910, 266, -28, 1, 16811, -22341, -21347, 13146, 2667, -2394, 462, -36, 1, 15551, 318149, -50400, -137435, 30135, 12999, -5460, 750, -45, 1, -1726511, -1415491, 2465969, 379940, -579590, 32109, 43659, -11220, 1155, -55

Offset: 0

R. J. Mathar, Jan 14 2025

			The table starts
       1
      -1        1
       1       -3        1
       1        7       -6        1
     -13       -5       25      -10        1
      47      -83      -60       65      -15        1
      73      637     -203     -280      140      -21        1
   -2447    -1425     3710       77     -910      266      -28        1
   16811   -22341   -21347    13146     2667    -2394      462      -36        1
   15551   318149   -50400  -137435    30135    12999    -5460      750      -45        1
-1726511 -1415491  2465969   379940  -579590    32109    43659   -11220     1155      -55        1

P. Wynn, Converging factors for the Weber parabolic cylinder functions of complex argument, part Ib, Proc. Konin. Ned. Akad. Weten., Series A, 66 (1963), 721-754 (two parts). Table VII.

Cf. A380170 (column s=1), A001664 (column s=2), A001662 (column s=0 apart from signs)

#re-using code of A001664
seq(seq( p(r,s),s=0..r),r=0..12) ;

cp's OEIS Frontend

A001663 Linear coefficient of the n-th converging polynomial of Weber functions (Erroneous version).

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A380170 Coefficient [k^1] of Wynn's converging polynomial p_n(k) of Weber functions.

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A380169 Table T(r,s) read by rows: the coefficient of [k^s] of the Wynn's r-th converging polynomial p_r(k) of Weber functions, 0<=s<=r.

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