A138415 Binomial transform of A000957.

0, 1, 2, 4, 10, 31, 110, 421, 1686, 6961, 29392, 126292, 550360, 2426503, 10803802, 48507844, 219377950, 998436793, 4569488372, 21016589074, 97090411020, 450314942683, 2096122733212, 9788916220519, 45850711498860, 215348942668681, 1013979873542690, 4785437476592806

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Transforms

Formula

From Vaclav Kotesovec, Oct 30 2017: (Start)

Recurrence: 2*n*a(n) = 3*(5*n - 6)*a(n-1) - (29*n - 57)*a(n-2) + 3*(7*n - 18)*a(n-3) - 5*(n-3)*a(n-4).

a(n) ~ 5^(n + 3/2) / (72 * sqrt(Pi) * n^(3/2)). (End)

Mathematica

Table[Sum[Binomial[n, k]*(2^k * (2*k-1)!! * Hypergeometric2F1Regularized[2, 2*k+1, k+2, -1] - 3*(-1)^k/2^(k+1)), {k, 1, n}], {n, 0, 30}] (* Vaclav Kotesovec, Oct 30 2017 *)
RecurrenceTable[{a[0]==0, a[1]==1, a[2]==2, a[3]==4, a[n]==(3(5n-6)a[n-1]-(29n-57) a[n-2]+3(7n-18)a[n-3]-5(n-3)a[n-4])/(2n)}, a, {n, 30}] (* Harvey P. Dale, Nov 22 2022 *)

Crossrefs

Cf. A000957, A138461.

Sequence in context: A007177 A328815 A242347 * A005268 A243931 A005269

Adjacent sequences: A138412 A138413 A138414 * A138416 A138417 A138418

Keyword

nonn

Author

N. J. A. Sloane, May 08 2008

Status

approved