A319365 Expansion of e.g.f. exp(x^4/4)/(1 - x).

1, 1, 2, 6, 30, 150, 900, 6300, 51660, 464940, 4649400, 51143400, 614968200, 7994586600, 111924212400, 1678863186000, 26865216378000, 456708678426000, 8220756211668000, 156194368021692000, 3123907159441068000, 65602050348262428000, 1443245107661773416000, 33194637476220788568000

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..449

Formula

a(n) ~ n!*exp(1/4).

(n+1)*(n+2)*(n+3)*(n+4)*a(n)-(n+2)*(n+3)*(n+4)*a(n+1)-(n+5)*a(n+4)+a(n+5)=0. - Robert Israel, Dec 28 2018

Maple

f:= gfun:-rectoproc({(n+1)*(n+2)*(n+3)*(n+4)*a(n)-(n+2)*(n+3)*(n+4)*a(n+1)-(n+5)*a(n+4)+a(n+5)}, seq(a(i)=[1, 1, 2, 6, 30][i+1], i=0..4)}, a(n), remember):
map(f, [$0..30]); # Robert Israel, Dec 28 2018

Mathematica

nmax = 23; CoefficientList[Series[Exp[x^4/4]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!

Prog

(Magma)  m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x^4/4)/(1-x))); [Factorial(n-1)*b[n]: n in [1..m]]; // Vincenzo Librandi, Dec 28 2018

Crossrefs

Cf. A000138, A000522, A030975, A060706, A130905, A319364.

Sequence in context: A113593 A122763 A166078 * A306946 A319104 A326756

Adjacent sequences: A319362 A319363 A319364 * A319366 A319367 A319368

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 17 2018

Status

approved