A363571 Expansion of (1 / sqrt(1 - 10*x + 9*x^2) - 1 / (1 - x)) / 4.

0, 1, 8, 61, 480, 3881, 31976, 266981, 2251136, 19124881, 163452168, 1403748941, 12104113632, 104723793721, 908680775528, 7904234296181, 68905275700736, 601832985410081, 5265459181363976, 46137526574521181, 404821208100919520, 3556361565584509001

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

E.g.f.: exp(x) * (exp(4*x) * BesselI(0,4*x) - 1) / 4.

a(n) = Sum_{k=1..n} binomial(n,k)^2 * 4^(k-1).

a(n) = (3^n * LegendreP(n,5/3) - 1) / 4.

a(n) = (A084771(n) - 1) / 4.

Mathematica

nmax = 21; CoefficientList[Series[(1/Sqrt[1 - 10 x + 9 x^2] - 1/(1 - x))/4, {x, 0, nmax}], x]
nmax = 21; CoefficientList[Series[Exp[x] (Exp[4 x] BesselI[0, 4 x] - 1)/4, {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Binomial[n, k]^2 4^(k - 1), {k, 1, n}], {n, 0, 21}]
Table[(3^n LegendreP[n, 5/3] - 1)/4, {n, 0, 21}]

Crossrefs

Cf. A030662, A047665, A084771, A098665, A363570.

Sequence in context: A278596 A190976 A254602 * A361772 A327761 A080525

Adjacent sequences: A363568 A363569 A363570 * A363572 A363573 A363574

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 17 2023

Status

approved