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A367330
a(n) = 27^n * Sum_{k=0..n} (-1)^k*binomial(-1/3, k)^2.
4
1, 24, 684, 17880, 493785, 13108608, 358702272, 9579537792, 261039317220, 6992695897440, 190104989730480, 5101807912472160, 138496042650288420, 3721234160086727040, 100918032317551270080, 2713823288825315967360, 73545091414048811297745
OFFSET
0,2
COMMENTS
In general, for m>1, Sum_{k>=0} (-1)^k * binomial(-1/m,k)^2 = 2^(-1/m) * sqrt(Pi) / (Gamma(1 - 1/(2*m)) * Gamma(1/2 + 1/(2*m))).
FORMULA
a(n) ~ Gamma(1/3)^3 * 3^(3*n+1) / (2^(8/3) * Pi^2).
MATHEMATICA
Table[27^n*Sum[(-1)^k*Binomial[-1/3, k]^2, {k, 0, n}], {n, 0, 16}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Nov 14 2023
STATUS
approved