A354640 -id:A354640 - cp's OEIS frontend

A354636 Decimal expansion of the negated digamma function at 1/9.

9, 4, 0, 7, 9, 4, 3, 2, 7, 7, 1, 3, 1, 8, 3, 1, 9, 1, 3, 2, 0, 3, 7, 5, 4, 0, 2, 9, 3, 3, 2, 6, 9, 8, 8, 7, 5, 2, 4, 2, 2, 2, 4, 0, 0, 4, 5, 8, 4, 3, 6, 5, 5, 5, 3, 0, 7, 7, 6, 0, 7, 2, 7, 7, 8, 1, 3, 6, 1, 5, 2, 1, 2, 3, 3, 8, 0, 7, 1, 8, 1, 9, 2, 1, 7, 2, 1, 0, 8, 4, 8, 8

Offset: 1

R. J. Mathar, Jun 01 2022

			psi(1/9) = -9.40794327713183...

Index entries for sequences related to the digamma function.

Cf. A354637, A354638, A354639, A354640, A354641.

RealDigits[PolyGamma[1/9], 10, 120][[1]] (* Amiram Eldar, Jun 14 2023 *)

PARI
```
-psi(1/9) \\ Amiram Eldar, Jun 14 2023
```

A354637 Decimal expansion of the negated digamma function at 2/9.

Original entry on oeis.org

4, 7, 6, 1, 2, 3, 5, 0, 7, 2, 7, 5, 5, 2, 3, 0, 7, 7, 0, 8, 4, 0, 2, 5, 9, 4, 1, 1, 5, 2, 7, 1, 5, 0, 1, 7, 3, 1, 3, 8, 5, 4, 8, 5, 3, 0, 7, 3, 6, 2, 2, 6, 8, 1, 7, 1, 5, 6, 8, 4, 2, 8, 4, 5, 4, 4, 5, 6, 2, 2, 3, 8, 3, 5, 7, 3, 7, 7, 6, 2, 7, 6, 0, 6, 2, 6, 4, 1, 6, 7, 7, 4

Offset: 1

R. J. Mathar, Jun 01 2022

			psi(2/9) = -4.76123507275523...

Index entries for sequences related to the digamma function.

Cf. A354636, A354638, A354639, A354640, A354641.

RealDigits[PolyGamma[2/9], 10, 120][[1]] (* Amiram Eldar, Jun 14 2023 *)

PARI
```
-psi(2/9) \\ Amiram Eldar, Jun 14 2023
```

A354638 Decimal expansion of the negated digamma function at 4/9.

Original entry on oeis.org

2, 2, 6, 6, 7, 6, 4, 1, 8, 7, 5, 6, 2, 8, 9, 8, 7, 8, 6, 5, 6, 4, 6, 3, 7, 5, 4, 9, 1, 3, 7, 7, 6, 1, 6, 0, 1, 8, 0, 8, 8, 3, 1, 4, 9, 5, 7, 1, 3, 6, 3, 7, 8, 4, 4, 8, 0, 5, 8, 8, 3, 5, 8, 2, 3, 3, 9, 8, 2, 1, 2, 0, 9, 0, 7, 7, 0, 7, 0, 8, 7, 5, 5, 7, 6, 6, 0, 6, 7, 1, 2

Offset: 1

R. J. Mathar, Jun 01 2022

			psi(4/9) = -2.266764187562...

Index entries for sequences related to the digamma function.

Cf. A354636, A354637, A354639, A354640, A354641.

RealDigits[PolyGamma[4/9], 10, 120][[1]] (* Amiram Eldar, Jun 14 2023 *)

PARI
```
-psi(4/9) \\ Amiram Eldar, Jun 14 2023
```

A354639 Decimal expansion of the negated digamma function at 5/9.

Original entry on oeis.org

1, 7, 1, 2, 8, 1, 6, 6, 4, 0, 3, 3, 9, 5, 1, 6, 0, 3, 0, 0, 1, 9, 6, 3, 4, 4, 8, 0, 2, 2, 0, 8, 5, 8, 1, 4, 8, 3, 5, 7, 4, 1, 9, 5, 1, 2, 8, 0, 8, 2, 6, 1, 3, 1, 1, 7, 7, 3, 1, 0, 2, 7, 1, 5, 8, 2, 9, 6, 6, 3, 0, 7, 1, 2, 0, 9, 2, 6, 7, 1, 2, 8, 8, 5, 3, 4, 3, 8, 7, 5, 3, 6

Offset: 1

R. J. Mathar, Jun 01 2022

			psi(5/9) = -1.71281664033951...

Index entries for sequences related to the digamma function.

Cf. A354636, A354637, A354638, A354640, A354641.

RealDigits[PolyGamma[5/9], 10, 120][[1]] (* Amiram Eldar, Jun 14 2023 *)

PARI
```
-psi(5/9) \\ Amiram Eldar, Jun 14 2023
```

A354641 Decimal expansion of the negated digamma function at 8/9.

Original entry on oeis.org

7, 7, 6, 4, 8, 8, 4, 0, 0, 2, 6, 9, 3, 4, 7, 6, 9, 0, 5, 3, 2, 8, 6, 4, 2, 6, 8, 9, 5, 4, 9, 0, 8, 1, 5, 8, 0, 6, 0, 5, 8, 9, 7, 7, 5, 8, 0, 6, 7, 9, 2, 6, 9, 2, 1, 4, 2, 7, 3, 6, 2, 4, 2, 5, 7, 8, 3, 4, 0, 1, 5, 2, 9, 9, 9, 9, 8, 7, 0, 3, 3, 9, 2, 0, 6, 9, 1, 4, 3, 7, 4

Offset: 0

R. J. Mathar, Jun 01 2022

			psi(8/9) = -0.77648840026934...

Index entries for sequences related to the digamma function.

Cf. A354636, A354637, A354638, A354639, A354640.

RealDigits[PolyGamma[8/9], 10, 120][[1]] (* Amiram Eldar, Jun 14 2023 *)

PARI
```
-psi(8/9) \\ Amiram Eldar, Jun 14 2023
```

A013656 a(n) = n(9n-2).

Original entry on oeis.org

0, 7, 32, 75, 136, 215, 312, 427, 560, 711, 880, 1067, 1272, 1495, 1736, 1995, 2272, 2567, 2880, 3211, 3560, 3927, 4312, 4715, 5136, 5575, 6032, 6507, 7000, 7511, 8040, 8587, 9152, 9735, 10336, 10955, 11592, 12247, 12920, 13611, 14320, 15047, 15792, 16555

Offset: 0

David W. Wilson

For n>0, numbers such that sqrt(a(n)) has the continued fraction {k;[1,1,1,2k]}, where the part in [] is repeated and k is of the form 3m+2 (A016789). - Bruno Berselli, May 30 2013

For n >= 1, the continued fraction expansion of sqrt(4*a(n)) is [6n-1; {3, 3n-1, 3, 12n-2}]. - Magus K. Chu, Sep 18 2022

G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A010701, A017257, A185019.

Cf. A016789, A061039, A144454.

[n*(9*n-2): n in [0..60]]; // G. C. Greubel, Mar 11 2022

Table[n(9n-2),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,7,32},50] (* Harvey P. Dale, Jul 07 2012 *)

a(n)=n*(9*n-2) \\ Charles R Greathouse IV, Jun 17 2017

a(n+1) = A144454(9*n+7) = A061039(27*n+21). - Paul Curtz, Nov 05 2008
a(n) = a(n-1) + 18*n - 11 with n>0, a(0)=0. - Vincenzo Librandi, Nov 22 2010
a(0)=0, a(1)=7, a(2)=32, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Jul 07 2012
From G. C. Greubel, Mar 11 2022: (Start)
G.f.: x*(7 - 11*x)/(1-x)^3.
E.g.f.: x*(7 + 9*x)*exp(x). (End)
Sum_{n>=1} 1/a(n) = -(psi(7/9)+gamma)/2 = (A354640-A001620)/2 = 0.22000753... - R. J. Mathar, Apr 22 2024

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A354636 Decimal expansion of the negated digamma function at 1/9.

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A354637 Decimal expansion of the negated digamma function at 2/9.

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A354638 Decimal expansion of the negated digamma function at 4/9.

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A354639 Decimal expansion of the negated digamma function at 5/9.

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A354641 Decimal expansion of the negated digamma function at 8/9.

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A013656 a(n) = n*(9*n-2).

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A013656 a(n) = n(9n-2).