The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A367885

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A367885

Expansion of e.g.f. 1/(1 - x * (exp(2*x) - 1)).
(history; published version)

#11 by Michael De Vlieger at Mon Dec 04 06:35:33 EST 2023

STATUS

proposed

approved

#10 by Seiichi Manyama at Mon Dec 04 05:34:03 EST 2023

STATUS

editing

proposed

#9 by Seiichi Manyama at Mon Dec 04 04:55:40 EST 2023

CROSSREFS

Cf. A337038, A351736.

#8 by Seiichi Manyama at Mon Dec 04 04:49:58 EST 2023

FORMULA

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

#7 by Seiichi Manyama at Mon Dec 04 04:46:46 EST 2023

FORMULA

a(0) = 1; a(n) = n! * Sum_{k=2..n} 2^(k-1)/(k-1)! * a(n-k)/(n-k)!.

#6 by Seiichi Manyama at Mon Dec 04 03:37:27 EST 2023

CROSSREFS

Cf. A351736.

#5 by Seiichi Manyama at Mon Dec 04 03:30:44 EST 2023

CROSSREFS

Cf. A052848, A367886.

#4 by Seiichi Manyama at Mon Dec 04 03:16:42 EST 2023

DATA

1, 0, 4, 12, 128, 1040, 12672, 161728, 2481152, 41806080, 791613440, 16399944704, 371591995392, 9110211874816, 240670782291968, 6810264853463040, 205583847590985728, 6593508525460226048, 223913466256013918208, 8026367531323488993280

#3 by Seiichi Manyama at Mon Dec 04 03:16:10 EST 2023

FORMULA

a(n) = n! * Sum_{k=0..floor(n/2)} 2^(n-k) * k! * Stirling2(n-k,k)/(n-k)!.

PROG

(PARI) a(n) = n!*sum(k=0, n\2, 2^(n-k)*k!*stirling(n-k, k, 2)/(n-k)!);

#2 by Seiichi Manyama at Mon Dec 04 03:13:31 EST 2023

NAME

allocated for Seiichi Manyama

Expansion of e.g.f. 1/(1 - x * (exp(2*x) - 1)).

DATA

1, 0, 4, 12, 128, 1040, 12672, 161728, 2481152, 41806080, 791613440, 16399944704, 371591995392, 9110211874816, 240670782291968

OFFSET

0,3

KEYWORD

allocated

nonn

AUTHOR

Seiichi Manyama, Dec 04 2023

STATUS

approved

editing