The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A372377

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A372377

Expansion of (1/x) * Series_Reversion( x * (1+x)^2 / (1+x+x^3)^3 ).
(history; published version)

#10 by Michael De Vlieger at Mon Apr 29 09:06:36 EDT 2024

STATUS

proposed

approved

#9 by Seiichi Manyama at Mon Apr 29 09:04:47 EDT 2024

STATUS

editing

proposed

#8 by Seiichi Manyama at Mon Apr 29 08:53:08 EDT 2024

FORMULA

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

PROG

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1+x)^2/(1+x+x^3)^3)/x)

#7 by Seiichi Manyama at Mon Apr 29 05:21:41 EDT 2024

DATA

1, 1, 1, 4, 13, 31, 91, 313, 988, 3095, 10377, 35146, 117682, 400117, 1381582, 4779997, 16599766, 58095076, 204319835, 720756820, 2552544940, 9074710255, 32356325145, 115679362789, 414701335849, 1490297002000, 5367227015647, 19369656905210, 70038419041844

#6 by Seiichi Manyama at Mon Apr 29 04:56:51 EDT 2024

NAME

Expansion of (1/x) * Series_Reversion( x * (1+x)^2 / (1+x+x^3)^3) ).

#5 by Seiichi Manyama at Mon Apr 29 04:13:02 EDT 2024

LINKS

<a href="/index/Res#revert">Index entries for reversions of series</a>

#4 by Seiichi Manyama at Mon Apr 29 04:02:55 EDT 2024

CROSSREFS

Cf. A372376, A372378.

#3 by Seiichi Manyama at Mon Apr 29 02:31:27 EDT 2024

PROG

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

#2 by Seiichi Manyama at Mon Apr 29 02:27:15 EDT 2024

NAME

allocated for Seiichi Manyama

Expansion of (1/x) * Series_Reversion( x * (1+x)^2 / (1+x+x^3)^3) ).

DATA

1, 1, 1, 4, 13, 31, 91, 313, 988, 3095, 10377, 35146, 117682, 400117, 1381582, 4779997, 16599766, 58095076, 204319835, 720756820, 2552544940, 9074710255, 32356325145, 115679362789, 414701335849

OFFSET

0,4

KEYWORD

allocated

nonn

AUTHOR

Seiichi Manyama, Apr 29 2024

STATUS

approved

editing

#1 by Seiichi Manyama at Mon Apr 29 02:27:15 EDT 2024

NAME

allocated for Seiichi Manyama

KEYWORD

allocated

STATUS

approved