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.

Showing 1-5 of 5 results.

A328866 Row sums of array A324124.

Original entry on oeis.org

1, 3, 15, 105, 945, 4158, 75075, 579150, 34459425, 339489150, 16499172690, 1724913508500, 878428175625, 131358797955000, 252664626678750, 3891675750482520, 221643095476699771875, 208605266331011550000, 32498195069133543750, 807994071847270157850000, 125885476393804690593030
Offset: 0

Views

Author

Petros Hadjicostas, Oct 29 2019

Keywords

Comments

These are the quantities D_n in Luke (1952). See the table on p. 217 of his paper. We use a(7) = 579150, which is a divisor of D_7 = 4054050. For an explanation of this change, see the comments for array A324124. (This modification does not change the values of the fractions gamma_r(n)/D_n used in Eq. (1) of Luke (1952). It is needed to give a unique definition of the terms of the array A324124.)

Links

Crossrefs

Cf. A002685, A002686, A324124, A328884, A328885.

A328884 Improved version of A002685; main diagonal of A324124.

Original entry on oeis.org

1, 2, 6, 34, 250, 972, 15498, 109544, 5961306, 54891535, 2488870076, 246264587430, 118503860254, 16917328320424, 31020551370600, 459016311081816, 25084010473396186126, 22789919291848918932, 3423598216929042597, 82480361346228654485320, 12440086312584102532500, 121292379506812780007192
Offset: 0

Views

Author

Petros Hadjicostas, Oct 29 2019

Keywords

Comments

Sequence A002685 has only 10 terms (from n = 1 to n = 10). We have a(n) = A002685(n) for 1 <= n <= 10 except for n = 7: a(7) = 109544 while A002685(7) = 766808 (which is a(7) * 7 = 109544 * 7). For an explanation, see the comments for array A324124. This is necessary to give a unique definition to the terms of array A324124.

Links

Crossrefs

Cf. A002685, A002686, A324124, A328866, A328885.

A328885 Improved version of A002686; secondary main diagonal of A324124.

Original entry on oeis.org

1, 8, 45, 416, 1685, 31032, 229026, 13856896, 132843888, 6551143600, 672567897859, 346984064352, 51233511973865, 99704578224832, 1521740934249300, 87595020192056292864, 81891555365769626429, 12883000343953567644, 318718123756704667891346, 50107182570391966040000, 500792393469899639083500
Offset: 1

Views

Author

Petros Hadjicostas, Oct 29 2019

Keywords

Comments

Sequence A002686 has only 10 terms (from n = 1 to n = 10). We have a(n) = A002686(n) for 1 <= n <= 10 except for n = 7: a(7) = 229026 while A002686(7) = 1603182 (which is a(7) * 7 = 229026 * 7). For an explanation, see the comments for array A324124. This is necessary to give a unique definition to the terms of array A324124.

Links

Crossrefs

Cf. A002685, A002686, A324124, A328866, A328884.

A002685 Coefficients for numerical integration.

Original entry on oeis.org

2, 6, 34, 250, 972, 15498, 766808, 5961306, 54891535, 2488870076
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

From Petros Hadjicostas, Oct 29 2019: (Start)
This is the main diagonal of A324124 (which is essentially the table on p. 217 in Luke (1952)), except that a(7) = 766808 must be replaced with 766808/7 = 109544. This is necessary to give a unique definition to the terms of A324124. For more information, see the comments for A324124.
Luke (1952) is not wrong (since 766808/4054050 = 109544/579150), but his integers for the case n = 7 have to modified as mentioned in the documentation of array A324124. For an improved version of this sequence, see A328884. (End)

References

  • 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).

Links

Crossrefs

Cf. A002686, A328866, A328884, A328885.
Main diagonal of A324124 (except for a(7)).

A002686 Coefficients for numerical integration.

Original entry on oeis.org

1, 8, 45, 416, 1685, 31032, 1603182, 13856896, 132843888, 6551143600
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

From Petros Hadjicostas, Oct 29 2019: (Start)
This is the secondary main diagonal of A324124 (which is essentially Table I on p. 217 in Luke (1952)), except that a(7) = 1603182 must be replaced with 1603182/7 = 229026. This is necessary to give a unique definition to the terms of A324124. For more information, see the comments for A324124.
Luke (1952) is not wrong (since 1603182/4054050 = 229026/579150), but his integers for the case n = 7 have to modified as mentioned in the documentation of array A324124. For an improved version of this sequence, see A328885. (End)

References

  • 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).

Links

Crossrefs

Cf. A002685, A328866, A328884, A328885.
Secondary diagonal of A324124 (except for a(7)).
Showing 1-5 of 5 results.

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

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