A362162 -id:A362162 - cp's OEIS frontend

A362155 Expansion of 1/(1 + x * (1-9*x)^(1/3)).

1, -1, 4, 2, 46, 221, 1627, 11312, 83704, 631433, 4868920, 38137757, 302694082, 2428593929, 19664122513, 160464212831, 1318266144163, 10893680220326, 90486907158265, 755060334587576, 6326283013232206, 53199259567645709, 448846559987031064

Offset: 0

Seiichi Manyama, Apr 09 2023

Cf. A039834, A362154.

Cf. A004987, A362157, A362162.

my(N=30, x='x+O('x^N)); Vec(1/(1+x*(1-9*x)^(1/3)))

a(n) = (-1)^n * Sum_{k=0..n} 9^k * binomial((n-k)/3,k).

a(n) ~ 3^(2*n-3) / (Gamma(2/3) * n^(4/3)). - Vaclav Kotesovec, Apr 10 2023

A362166 Expansion of e.g.f. exp(-x * (1-3*x)^(1/3)).

Original entry on oeis.org

1, -1, 3, -1, 41, 299, 4531, 74507, 1474481, 33540119, 864507491, 24891022199, 791755864153, 27571976573699, 1043247441846611, 42615848603499779, 1869129393654945761, 87605345727468933167, 4369604246576366377411, 231091472431638655755119

Offset: 0

Seiichi Manyama, Apr 10 2023

Cf. A362162, A362164.

A362166 := proc(n)
    (-1)^n*n!*add(3^k * binomial((n-k)/3,k)/(n-k)!,k=0..n) ;
end proc:
seq(A362166(n),n=0..70) ; # R. J. Mathar, Dec 04 2023

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-3*x)^(1/3))))

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

D-finite with recurrence +(-9*n+11)*a(n) +2*(27*n^2-121*n+72)*a(n-1) +3*(-27*n^3+304*n^2-1053*n+1056)*a(n-2) +(-612*n^3+6984*n^2-23677*n+21227) *a(n-3) +4*(27*n-23)*(n-3)*a(n-4) -48*(9*n-10) *(n-3)*(n-4) *a(n-5) +64*(n-5)*(n-4)*(9*n^2-62*n+78)*a(n-6) +256*(n-5) *(n-6)*(17*n-24)*(n-4)*a(n-7)=0. - R. J. Mathar, Dec 04 2023

cp's OEIS Frontend

A362155 Expansion of 1/(1 + x * (1-9*x)^(1/3)).

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