A344055 a(n) = 2^n * n! * [x^n](exp(2*x) * BesselI(1, x)).

0, 1, 8, 51, 304, 1770, 10224, 58947, 340064, 1964862, 11374000, 65966318, 383289504, 2230877428, 13005037920, 75923905635, 443837331648, 2597761611894, 15221636471088, 89283411393018, 524194439193120, 3080311943546124, 18115458433730592, 106618075368243534

Offset

0,3

Links

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

Formula

a(n) = [x^n] (1/(2*x))*(1 - (4*x - 1)/(sqrt((6*x - 1)*(2*x - 1)))).

D-finite with recurrence a(n) = 4*(3*(n^2 - n)*a(n - 2) - (2*n^2 - n)*a(n - 1))/(1 - n^2) for n >= 2.

The INVERT transform of A052177.

a(n) ~ 2^(n - 1/2) * 3^(n + 1/2) / sqrt(Pi*n). - Vaclav Kotesovec, May 12 2021

Maple

gf := exp(2*x)*BesselI(1, x):
ser := series(gf, x, 32): seq(2^n*n!*coeff(ser, x, n), n = 0..23);
# Or:
gf := (1/(2*x))*(1 - (4*x - 1)/(sqrt((6*x - 1)*(2*x - 1)))):
ser := series(gf, x, 32): seq(coeff(ser, x, n), n = 0..23);

Mathematica

RecurrenceTable[{(1 - n^2) a[n] == 4 (3 (n^2 - n) a[n - 2] - (2 n^2 - n) a[n - 1]), a[0] == 0, a[1] == 1}, a, {n, 0, 23}]

Crossrefs

Cf. A052177.

Sequence in context: A295348 A082135 A153594 * A316594 A037697 A037606

Adjacent sequences: A344052 A344053 A344054 * A344056 A344057 A344058

Keyword

nonn,easy

Author

Peter Luschny, May 12 2021

Status

approved