A186859 E.g.f. A(x)=exp(x^6+3*x^5+4*x^4+3*x^3+2*x^2+x).

1, 1, 5, 31, 241, 2021, 19741, 224155, 2816801, 38127241, 557512021, 8805585911, 148896471505, 2668912291501, 50505733789421, 1007422798667251, 21118304040298561, 463416656527980305, 10612758078821689381, 253157568544420465231, 6279192326923499850161

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..470

Kruchinin Vladimir Victorovich, Composition of ordinary generating functions, arXiv:1009.2565 [math.CO], 2010.

Formula

a(n) = n!*Sum(m=1..n, Sum(k=m..n, binomial(k,n-k)*Sum(j=0..m, binomial(m,j)*binomial(j,k-3*m+2*j)))/m!).

From Benedict W. J. Irwin, Jun 02 2016: (Start)

Let y(0)=1, y(1)=1, y(2)=5/2, y(3)=31/6, y(4)=241/24, y(5)=2021/120,

Let -6*y(n)-15*y(n+1)-16*y(n+2)-9*y(n+3)-4*y(n+4)-y(n+5)+(n+6)y(n+6)=0,

a(n) = n!y(n).

(End)

Example

G.f. = 1 + x + 5*x^2 + 31*x^3 + 241*x^4 + 2021*x^5 + 19741*x^6 + 224155*x^7 + ...

Mathematica

With[{nn=20}, CoefficientList[Series[E^(x^6+3x^5+4x^4+3x^3+2x^2+x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jan 26 2014 *)

Prog

(PARI) {a(n) = if( n<0, 0, n! * polcoeff( exp(x^6 + 3*x^5 + 4*x^4 + 3*x^3 + 2*x^2 + x + x * O(x^n)), n))}; /* Michael Somos, Jun 04 2016 */
(Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(x^6+3*x^5+4*x^4+3*x^3+2*x^2+x))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 14 2018

Crossrefs

Sequence in context: A211179 A177797 A293717 * A331335 A082579 A294214

Adjacent sequences: A186856 A186857 A186858 * A186860 A186861 A186862

Keyword

nonn

Author

Vladimir Kruchinin, Feb 28 2011

Extensions

More terms from Harvey P. Dale, Jan 26 2014

Status

approved