The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A366071 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A366071

Expansion of (1/x) * Series_Reversion( x*(1+x-x^3)/(1+x) ).
(history; published version)

#13 by Michael De Vlieger at Fri Sep 29 10:04:25 EDT 2023

STATUS

reviewed

approved

#12 by Joerg Arndt at Fri Sep 29 09:27:57 EDT 2023

STATUS

proposed

reviewed

#11 by Seiichi Manyama at Fri Sep 29 08:50:44 EDT 2023

STATUS

editing

proposed

#10 by Seiichi Manyama at Fri Sep 29 07:22:12 EDT 2023

CROSSREFS

Cf. A054514.

#9 by Seiichi Manyama at Fri Sep 29 07:18:54 EDT 2023

FORMULA

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (-1)^(n-k) * binomial(n+k,k) * binomial(n-2*k-1,n-3*k).

#8 by Seiichi Manyama at Fri Sep 29 07:13:06 EDT 2023

CROSSREFS

Cf. A366101, A366102.

#7 by Seiichi Manyama at Fri Sep 29 07:06:52 EDT 2023

DATA

1, 0, 0, 1, -1, 1, 3, -8, 14, 1, -49, 144, -162, -139, 1159, -2532, 2036, 6062, -26282, 47440, -11474, -190071, 606163, -838984, -481092, 5479390, -13618658, 13030368, 28786262, -148598623, 294393355, -128639411, -1086088045, 3848604261, -5935686369, -1750697623

#6 by Seiichi Manyama at Fri Sep 29 07:06:22 EDT 2023

PROG

(PARI) a(n) = sum(k=0, n\3, (-1)^(n-k)*binomial(n+k, k)*binomial(n-2*k-1, n-3*k))/(n+1);

#5 by Seiichi Manyama at Fri Sep 29 06:44:16 EDT 2023

CROSSREFS

Cf. A366095, A366096, A366097.

Cf. A366101.

#4 by Seiichi Manyama at Fri Sep 29 06:32:42 EDT 2023

NAME

allocated for Seiichi Manyama

Expansion of (1/x) * Series_Reversion( x*(1+x-x^3)/(1+x) ).

DATA

1, 0, 0, 1, -1, 1, 3, -8, 14, 1, -49, 144, -162, -139, 1159, -2532, 2036, 6062, -26282, 47440, -11474, -190071, 606163, -838984, -481092, 5479390

OFFSET

0,7

KEYWORD

allocated

sign

AUTHOR

Seiichi Manyama, Sep 29 2023

STATUS

approved

editing