A352469 a(0) = 1; a(n) = (1/n) * Sum_{k=0..floor((n-1)/2)} binomial(n,2*k+1)^3 * (2*k+1) * a(n-2*k-1).

1, 1, 4, 37, 640, 18401, 810616, 51506645, 4512303104, 526359723265, 79484297525704, 15182084413118525, 3598056798827450752, 1040872295660542894433, 362422517793599461361216, 150047916077302216370174237, 73081847594180657956494147584, 41481744863993143666887680079873

Offset

0,3

Links

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

Formula

Sum_{n>=0} a(n) * x^n / n!^3 = exp( Sum_{n>=0} x^(2*n+1) / (2*n+1)!^3 ).

Mathematica

a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, 2 k + 1]^3 (2 k + 1) a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 17}]
nmax = 17; CoefficientList[Series[Exp[Sum[x^(2 k + 1)/(2 k + 1)!^3, {k, 0, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!^3

Crossrefs

Cf. A003724, A061684, A346220, A352466.

Sequence in context: A155926 A094408 A348860 * A061683 A084283 A163880

Adjacent sequences: A352466 A352467 A352468 * A352470 A352471 A352472

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 17 2022

Status

approved