A336606 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(x) / BesselJ(0,2*sqrt(x)).

1, 2, 9, 70, 851, 15246, 384147, 13065354, 578905875, 32440563766, 2243907466283, 187796863841346, 18704441632101337, 2186374265471576090, 296396762529435076953, 46126320892158605384334, 8167358455139620845210003, 1632571811017090501346518086

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = n! * Sum_{k=0..n} binomial(n,k) * A000275(k) / k!.

a(n) ~ Pi * 2^(2*n+2) * n^(2*n+1) / (BesselJ(1, r) * exp(2*n - r^2/4) * r^(2*n+1)), where r = BesselJZero(0,1) = A115368. - Vaclav Kotesovec, Feb 09 2026

Mathematica

nmax = 17; CoefficientList[Series[Exp[x]/BesselJ[0, 2 Sqrt[x]], {x, 0, nmax}], x] Range[0, nmax]!^2
A000275[0] = 1; A000275[n_] := A000275[n] = -Sum[(-1)^(n - k) Binomial[n, k]^2 A000275[k], {k, 0, n - 1}]; a[n_] := n! Sum[Binomial[n, k] A000275[k]/k!, {k, 0, n}]; Table[a[n], {n, 0, 17}]

Crossrefs

Cf. A000275, A002720, A009940, A336608.

Cf. A115368.

Sequence in context: A322772 A177450 A193469 * A121879 A118789 A386452

Adjacent sequences: A336603 A336604 A336605 * A336607 A336608 A336609

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 27 2020

Status

approved