A336589 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(x) * BesselI(0,2*sqrt(1 - exp(x))).

1, 0, -3, -19, -75, 574, 25795, 579963, 9342529, 21955076, -7954085799, -535479422655, -25206613635203, -871888114433454, -7465407495946777, 2538884115164554199, 344689220434285963905, 31689538033223254172648, 2273498459548301881979029

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = n! * Sum_{k=0..n} (-1)^k * Stirling2(n+1,k+1) / k!.

Mathematica

nmax = 18; CoefficientList[Series[Exp[x] BesselI[0, 2 Sqrt[1 - Exp[x]]], {x, 0, nmax}], x] Range[0, nmax]!^2
Table[n! Sum[(-1)^k StirlingS2[n + 1, k + 1]/k!, {k, 0, n}], {n, 0, 18}]

Prog

(PARI) a(n) = n! * sum(k=0, n, (-1)^k*stirling(n+1, k+1, 2) / k!); \\ Michel Marcus, Jul 29 2020

Crossrefs

Cf. A001569, A009940, A293037, A336588.

Sequence in context: A247059 A243142 A174286 * A240746 A027175 A093734

Adjacent sequences: A336586 A336587 A336588 * A336590 A336591 A336592

Keyword

sign

Author

Ilya Gutkovskiy, Jul 26 2020

Status

approved