cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Andrew J. Robbins

Andrew J. Robbins's wiki page.

Andrew J. Robbins has authored 4 sequences.

A157504 (det(I - M) - 1)/x where M_jk = (j*x)^k/k!.

Original entry on oeis.org

-1, -2, -7, -40, -301, -2856, -32299, -416816, -5892345, -86464000, -1177909711, -8944121088, 349846341467, 29237270702080, 1585383533246925, 78578098584541184, 3843296406581515919, 190784066705549623296
Offset: 1

Views

Author

Andrew J. Robbins, Mar 02 2009

Keywords

Crossrefs

Cf. A157503.

Formula

E.g.f.: (det(I - M) - 1)/x where M_jk = (j*x)^k/k!.
a(n) = A157503(n)/n.

A157503 det(I - M) where M_jk = (j*x)^k/k!.

Original entry on oeis.org

1, -1, -4, -21, -160, -1505, -17136, -226093, -3334528, -53031105, -864640000, -12957006821, -107329453056, 4548002439071, 409321789829120, 23780752998703875, 1257249577352658944, 65336038911885770623
Offset: 0

Views

Author

Andrew J. Robbins, Mar 02 2009

Keywords

Comments

The n X n matrix M is a Vandermonde matrix of (x, 2x, 3x, ..., j*x, ..., n*x) scaled by factorials. The first n coefficients of x in det(I - M) are always the same.

Links

Programs

  • Mathematica
    A[n_] := D[Det[Table[KroneckerDelta[j,k] - (j*x)^k/k!, {j,1,n}, {k,1,n}]], {x, n}]/.x->0

Formula

E.g.f.: det(I - M) where M_jk = (j*x)^k/k!.

A170874 Hexadecimal expansion of Euler-Mascheroni constant gamma.

Original entry on oeis.org

9, 3, 12, 4, 6, 7, 14, 3, 7, 13, 11, 0, 12, 7, 10, 4, 13, 1, 11, 14, 3, 15, 8, 1, 0, 1, 5, 2, 12, 11, 5, 6, 10, 1, 12, 14, 12, 12, 3, 10, 15, 6, 5, 12, 12, 0, 1, 9, 0, 12, 0, 3, 13, 15, 3, 4, 7, 0, 9, 10, 15, 15, 11, 13, 8, 14, 4, 11, 5, 9, 15, 10, 0, 3, 10, 9, 15, 0, 14, 14, 13, 0, 6, 4, 9, 12
Offset: 0

Views

Author

Andrew J. Robbins, Jan 03 2010, at the request of N. J. A. Sloane

Keywords

Examples

			.93C467E37DB0C7A4D1BE3F810152CB56A1CECC3AF65CC0190C03DF34709AFFBD8E4B5...

Crossrefs

Cf. A104015, A001620.

Programs

  • Mathematica
    RealDigits[EulerGamma~N~200, 16][[1]]

Formula

a(n) = 8*A104015(4n)+4*A104015(4n+1)+2*A104015(4n+2)+1*A104015(4n+3).

A170873 Hexadecimal expansion of e.

Original entry on oeis.org

2, 11, 7, 14, 1, 5, 1, 6, 2, 8, 10, 14, 13, 2, 10, 6, 10, 11, 15, 7, 1, 5, 8, 8, 0, 9, 12, 15, 4, 15, 3, 12, 7, 6, 2, 14, 7, 1, 6, 0, 15, 3, 8, 11, 4, 13, 10, 5, 6, 10, 7, 8, 4, 13, 9, 0, 4, 5, 1, 9, 0, 12, 15, 14, 15, 3, 2, 4, 14, 7, 7, 3, 8, 9, 2, 6, 12, 15, 11, 14, 5, 15, 4, 11, 15, 8, 13, 8
Offset: 1

Views

Author

Andrew J. Robbins, Jan 03 2010, at the request of N. J. A. Sloane

Keywords

Examples

			2.B7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF324E...

Crossrefs

Cf. A004593, A001113.
Expansion of e in base b: A004593 (b=2), A004594 (b=3), A004595 (b=4), A004596 (b=5), A004597 (b=6), A004598 (b=7), A004599 (b=8), A004600 (b=9), A001113 (b=10), this sequence (b=16). - Jason Kimberley, Dec 05 2012

Programs

  • Mathematica
    RealDigits[E~N~200, 16][[1]]
RealDigits[E,16,120][[1]] (* Harvey P. Dale, Mar 21 2023 *)

Formula

a(n) = 8*A004593(4n)+4*A004593(4n+1)+2*A004593(4n+2)+1*A004593(4n+3).

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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