A182967 E.g.f.: A(x) = Product_{n>=1} (1 + 4*x^n/n)^n.

1, 4, 8, 120, 576, 6240, 75840, 772800, 11585280, 163914240, 2694558720, 45947489280, 876665180160, 17329568256000, 364677585592320, 8306018798837760, 195321474697789440, 4892032896606535680

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..436

Example

E.g.f.: A(x) = 1 + 4*x + 8*x^2/2! + 120*x^3/3! + 576*x^4/4! +...
A(x) = (1+4x)*(1+4x^2/2)^2*(1+4x^3/3)^3*(1+4x^4/4)^4*(1+4x^5/5)^5*...

Mathematica

With[{nn=20}, CoefficientList[Series[Product[(1+4 x^n/n)^n, {n, nn}], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Apr 11 2020 *)

Prog

(PARI) {a(n, k=4)=n!*polcoeff(prod(m=1, n, (1+k*x^m/m+x*O(x^n))^m), n)}

Crossrefs

Cf. A181541, A182965, A182966, A007838.

Sequence in context: A111100 A105036 A012940 * A013049 A193155 A060239

Adjacent sequences: A182964 A182965 A182966 * A182968 A182969 A182970

Keyword

nonn

Author

Paul D. Hanna, Dec 19 2010

Status

approved