The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A349524 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A349524

a(n) = Sum_{k=0..n} (2*k+1)^(k-1) * Stirling2(n,k).
(history; published version)

#36 by Alois P. Heinz at Fri Jul 29 08:42:15 EDT 2022

STATUS

editing

approved

#35 by Alois P. Heinz at Fri Jul 29 08:42:12 EDT 2022

MAPLE

b:= proc(n, m) option remember; `if`(n=0,

(2*m+1)^(m-1), m*b(n-1, m)+b(n-1, m+1))

end:

a:= n-> b(n, 0):

seq(a(n), n=0..24); # Alois P. Heinz, Jul 29 2022

STATUS

approved

editing

#34 by Andrew Howroyd at Sat Nov 27 11:28:55 EST 2021

STATUS

reviewed

approved

#33 by Joerg Arndt at Sat Nov 27 05:00:45 EST 2021

STATUS

proposed

reviewed

#32 by Michel Marcus at Sat Nov 27 02:36:57 EST 2021

STATUS

editing

proposed

#31 by Michel Marcus at Sat Nov 27 02:36:46 EST 2021

CROSSREFS

Cf. A000110, A008277, A052880, A349504, A349525.

STATUS

approved

editing

Discussion

Sat Nov 27

02:36

Michel Marcus: A008277

#30 by Peter Luschny at Sun Nov 21 04:21:38 EST 2021

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reviewed

approved

#29 by Michel Marcus at Sun Nov 21 04:10:57 EST 2021

STATUS

proposed

reviewed

#28 by Seiichi Manyama at Sun Nov 21 03:54:53 EST 2021

STATUS

editing

proposed

#27 by Seiichi Manyama at Sun Nov 21 03:51:29 EST 2021

FORMULA

From _G.f.: Sum_{k>=0} (2*k+1)^(k-1) * x^k/Product_{j=1..k} (1 - j*x). - _Seiichi Manyama_, Nov 20 2021: (Start)

a(0) = 1; a(n) = Sum_{k=1..n} (2*k+1)^(k-1) * binomial(n-1,k-1) * a(n-k).

G.f.: Sum_{k>=0} (2*k+1)^(k-1) * x^k/Product_{j=1..k} (1 - j*x). (End)

PROG

(PARI) a(n) = if(n==0, 1, sum(k=1, n, (2*k+1)^(k-1)*binomial(n-1, k-1)*a(n-k))); \\ Seiichi Manyama, Nov 20 2021

STATUS

approved

editing

Discussion

Sun Nov 21

03:54

Seiichi Manyama: @Vaclav Kotesovec: Sorry, my second pari program was wrong.