The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A365609 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A365609

G.f. satisfies A(x) = 1 + x^2*A(x)^4*(1 + x*A(x)).
(history; published version)

#25 by Michael De Vlieger at Sun Sep 17 10:11:10 EDT 2023

STATUS

reviewed

approved

#24 by Joerg Arndt at Sun Sep 17 09:01:32 EDT 2023

STATUS

proposed

reviewed

#23 by Seiichi Manyama at Sun Sep 17 08:54:46 EDT 2023

STATUS

editing

proposed

#22 by Seiichi Manyama at Sun Sep 17 06:59:15 EDT 2023

FORMULA

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

#21 by Seiichi Manyama at Sun Sep 17 06:58:50 EDT 2023

DATA

1, 0, 1, 1, 4, 9, 27, 78, 231, 715, 2193, 6954, 21999, 70840, 228896, 746650, 2447757, 8072208, 26745627, 89002364, 297344960, 996865397, 3352918429, 11310307593, 38256171642, 129718262583, 440855654827, 1501451066767, 5123671576890, 17516503865294

#20 by Seiichi Manyama at Sun Sep 17 06:58:08 EDT 2023

PROG

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

#19 by Seiichi Manyama at Sun Sep 17 06:55:08 EDT 2023

CROSSREFS

Cf. A001005, A025250, A055113, A217358.

#18 by Seiichi Manyama at Sun Sep 17 06:52:48 EDT 2023

NAME

allocated for Seiichi Manyama

G.f. satisfies A(x) = 1 + x^2*A(x)^4*(1 + x*A(x)).

DATA

1, 0, 1, 1, 4, 9, 27, 78, 231, 715, 2193, 6954, 21999, 70840, 228896, 746650, 2447757, 8072208, 26745627, 89002364, 297344960, 996865397, 3352918429, 11310307593, 38256171642, 129718262583

OFFSET

0,5

CROSSREFS

Cf. A365690.

KEYWORD

allocated

nonn

AUTHOR

Seiichi Manyama, Sep 17 2023

STATUS

approved

editing

#17 by Seiichi Manyama at Sun Sep 17 06:52:48 EDT 2023

NAME

allocated for Seiichi Manyama

KEYWORD

recycled

allocated

#16 by Michel Marcus at Sun Sep 17 02:32:49 EDT 2023

STATUS

reviewed

approved