The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A144048

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A144048

Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is Euler transform of (j->j^k).
(history; published version)

#36 by Alois P. Heinz at Fri Sep 23 16:13:04 EDT 2022

STATUS

proposed

approved

#35 by Jon E. Schoenfield at Fri Sep 23 16:05:42 EDT 2022

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editing

proposed

#34 by Jon E. Schoenfield at Fri Sep 23 15:55:30 EDT 2022

COMMENTS

In general, column k > 0 is asymptotic to (GAMMAGamma(k+2)*Zeta(k+2))^((1-2*Zeta(-k)) /(2*k+4)) * exp((k+2)/(k+1) * (GAMMAGamma(k+2)*Zeta(k+2))^(1/(k+2)) * n^((k+1)/(k+2)) + Zeta'(-k)) / (sqrt(2*Pi*(k+2)) * n^((k+3-2*Zeta(-k))/(2*k+4))). - Vaclav Kotesovec, Mar 01 2015

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approved

editing

#33 by Alois P. Heinz at Mon Sep 24 08:46:00 EDT 2018

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editing

approved

#32 by Alois P. Heinz at Mon Sep 24 08:45:17 EDT 2018

EXAMPLE

1, 1, 1, 1, 1, 1, ...

2, 3, 5, 9, 17, 33, ...

3, 6, 14, 36, 98, 276, ...

5, 13, 40, 136, 490, 1828, ...

7, 24, 101, 477, 2411, 12729, ...

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approved

editing

#31 by Alois P. Heinz at Wed Jul 19 21:06:07 EDT 2017

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editing

approved

#30 by Alois P. Heinz at Wed Jul 19 21:06:03 EDT 2017

LINKS

Vaclav Kotesovec, <a href="httphttps://arxiv.org/abs/1509.08708">A method of finding the asymptotics of q-series based on the convolution of generating functions</a>, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 21.

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approved

editing

#29 by Bruno Berselli at Thu Mar 09 05:29:27 EST 2017

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proposed

approved

#28 by Seiichi Manyama at Thu Mar 09 00:04:44 EST 2017

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editing

proposed

#27 by Seiichi Manyama at Thu Mar 09 00:04:21 EST 2017

CROSSREFS

Cf. A283272.

STATUS

proposed

editing