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Revision History for A370275 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing all changes.
Coefficient of x^n in the expansion of 1/( (1-x)^2 * (1-x^3)^2 )^n.
(history; published version)
#9 by Michael De Vlieger at Wed Feb 14 10:48:24 EST 2024
STATUS

proposed

approved

#8 by Seiichi Manyama at Wed Feb 14 07:42:16 EST 2024
STATUS

editing

proposed

#7 by Seiichi Manyama at Wed Feb 14 07:38:24 EST 2024
CROSSREFS

Cf. A369298.

#6 by Seiichi Manyama at Tue Feb 13 21:52:44 EST 2024
FORMULA

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

#5 by Seiichi Manyama at Tue Feb 13 21:42:37 EST 2024
FORMULA

a(n) = Sum_{k=0..floor(n/3)}

The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x)^2 * (1-x^3)^2 ). See A369298.

#4 by Seiichi Manyama at Tue Feb 13 21:33:03 EST 2024
DATA

1, 2, 10, 62, 394, 2552, 16822, 112310, 756874, 5137676, 35076360, 240606082, 1656906550, 11447855850, 79319081054, 550925792312, 3834743187594, 26742188401900, 186802789016908, 1306827910585782, 9154542088193544, 64206944261628146, 450823141806229290

#3 by Seiichi Manyama at Tue Feb 13 21:32:29 EST 2024
PROG

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

#2 by Seiichi Manyama at Tue Feb 13 21:32:07 EST 2024
NAME

allocated for Seiichi ManyamaCoefficient of x^n in the expansion of 1/( (1-x)^2 * (1-x^3)^2 )^n.

DATA

1, 2, 10, 62, 394, 2552, 16822, 112310, 756874, 5137676, 35076360, 240606082, 1656906550, 11447855850, 79319081054, 550925792312

OFFSET

0,2

KEYWORD

allocated

nonn

AUTHOR

Seiichi Manyama, Feb 13 2024

STATUS

approved

editing

#1 by Seiichi Manyama at Tue Feb 13 21:32:07 EST 2024
NAME

allocated for Seiichi Manyama

KEYWORD

allocated

STATUS

approved