The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A372233

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A372233

Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x-x^2) )^n.
(history; published version)

#47 by Vaclav Kotesovec at Sat May 04 04:46:09 EDT 2024

STATUS

editing

approved

#46 by Vaclav Kotesovec at Sat May 04 04:45:52 EDT 2024

FORMULA

a(n) ~ sqrt((1/8 + cos(arccos(sqrt(37)/8)/3)/sqrt(37))/(Pi*n)) / (-2/3 + sqrt(35/18)*cos(arccos(-4537/(560*sqrt(70)))/3))^n. - Vaclav Kotesovec, May 04 2024

#45 by Vaclav Kotesovec at Sat May 04 04:26:06 EDT 2024

CROSSREFS

Cf. A213684, A236339, A372458, A372460.

#44 by Vaclav Kotesovec at Sat May 04 04:25:17 EDT 2024

MATHEMATICA

Table[SeriesCoefficient[1/((1-x)*(1-x-x^2))^n, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, May 04 2024 *)

STATUS

approved

editing

#43 by R. J. Mathar at Thu May 02 12:20:25 EDT 2024

STATUS

editing

approved

#42 by R. J. Mathar at Thu May 02 12:20:15 EDT 2024

FORMULA

D-finite with recurrence +575*n*(n-1)*(n-2)*a(n) +40*(n-1)*(n-2)*(125*n-178)*a(n-1) -16*(n-2)*(3272*n^2-5536*n+75)*a(n-2) +8*(-22112*n^3+169392*n^2-450082*n+415827)*a(n-3) +1344*(96*n^3-1328*n^2+5794*n-8139)*a(n-4) +3072*(4*n-15)*(2*n-9)*(4*n-17)*a(n-5)=0. - R. J. Mathar, May 02 2024

MAPLE

A372233 := proc(n)

add(binomial(n+k-1, k) * binomial(3*n-k-1, n-2*k), k=0..floor(n/2));

end proc:

seq(A372233(n), n=0..50) ; # R. J. Mathar, May 02 2024

STATUS

approved

editing

#41 by Michael De Vlieger at Thu May 02 09:46:37 EDT 2024

STATUS

proposed

approved

#40 by Seiichi Manyama at Thu May 02 08:42:55 EDT 2024

STATUS

editing

proposed

#39 by Seiichi Manyama at Thu May 02 08:37:41 EDT 2024

CROSSREFS

Cf. A236339, A372458, A372460.

#38 by Seiichi Manyama at Thu May 02 08:24:26 EDT 2024

FORMULA

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