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Revision History for A014160

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A014160

Apply partial sum operator thrice to partition numbers.
(history; published version)

#34 by Sean A. Irvine at Mon Mar 20 17:37:47 EDT 2023

STATUS

proposed

approved

#33 by Michel Marcus at Thu Mar 02 01:54:20 EST 2023

STATUS

editing

proposed

#32 by Michel Marcus at Thu Mar 02 01:54:15 EST 2023

FORMULA

O.g.f.: 1/(1 - x)^3 * product Product_{k >= 1} 1/(1 - x^k).

STATUS

proposed

editing

#31 by Jon E. Schoenfield at Wed Mar 01 23:18:04 EST 2023

STATUS

editing

proposed

#30 by Jon E. Schoenfield at Wed Mar 01 23:18:02 EST 2023

AUTHOR

N. J. A. Sloane.

STATUS

proposed

editing

#29 by Jon E. Schoenfield at Wed Mar 01 23:17:55 EST 2023

STATUS

editing

proposed

#28 by Jon E. Schoenfield at Wed Mar 01 23:17:53 EST 2023

FORMULA

a(n-1) + a(n-2) = sum Sum_{parts k in all partitions of n} J_2(k), where J_2(n) is the Jordan totient function A007434(n). (End)

STATUS

proposed

editing

#27 by Omar E. Pol at Wed Mar 01 18:41:45 EST 2023

STATUS

editing

proposed

#26 by Omar E. Pol at Wed Mar 01 18:41:42 EST 2023

COMMENTS

Partial sums of A014153.

STATUS

proposed

editing

#25 by Omar E. Pol at Wed Mar 01 18:31:29 EST 2023

STATUS

editing

proposed