A366433 G.f. A(x) satisfies A(x) = 1 + x * ((1 - x) / A(x))^(3/2).

1, 1, -3, 9, -37, 171, -849, 4421, -23820, 131676, -742616, 4255944, -24714276, 145103426, -859920585, 5137093695, -30902681230, 187034086170, -1138106903928, 6958662440416, -42729903714420, 263400623938140, -1629378251621535, 10111374706286895

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(5*k/2-1,k) * binomial(3*k/2,n-k) / (5*k/2-1).

a(n) ~ -(-1)^n * sqrt(4*10^(1/3) + 10^(2/3) - 5) * 3^(n + 1/2) * 5^(n-1) / (sqrt(Pi) * (2 + 10^(1/3)) * n^(3/2) * (4*10^(1/3) + 10^(2/3) - 11)^n). - Vaclav Kotesovec, Oct 10 2023

Mathematica

Table[(-1)^(n-1) * Sum[Binomial[5*k/2 - 1, k]*Binomial[3*k/2, n - k]/(5*k/2 - 1), {k, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Oct 10 2023 *)

Prog

(PARI) a(n) = (-1)^(n-1)*sum(k=0, n, binomial(5*k/2-1, k)*binomial(3*k/2, n-k)/(5*k/2-1));

Crossrefs

Partial sums give A366404.

Cf. A366431, A366432, A366434, A366435, A366436, A366437.

Sequence in context: A245890 A119856 A077365 * A319119 A006229 A321734

Adjacent sequences: A366430 A366431 A366432 * A366434 A366435 A366436

Keyword

sign

Author

Seiichi Manyama, Oct 09 2023

Status

approved