A277175 Convolution of Catalan numbers and factorial numbers.

1, 2, 5, 15, 53, 222, 1120, 6849, 50111, 427510, 4142900, 44693782, 529276962, 6813205468, 94642629984, 1410507388421, 22445134308123, 379776665469030, 6808016435182620, 128886547350655050, 2569493300908367550, 53805226930896987540, 1180673761078007109840

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..449

Formula

a(n) = Sum_{i=0..n} C(i) * (n-i)!.

a(n) ~ n! * (1 + 1/n + 2/n^2 + 7/n^3 + 31/n^4 + 163/n^5 + 979/n^6 + 6556/n^7 + 48150/n^8 + 383219/n^9 + 3275121/n^10 + ...), for coefficients see A277396. - Vaclav Kotesovec, Oct 13 2016

Maple

a:= proc(n) option remember; `if`(n<4, [1, 2, 5, 15][n+1],
      ((2*(n^4-n^3-19*n^2+48*n-5))*a(n-1)
       -(n+1)*(n^4+9*n^3-90*n^2+226*n-160)*a(n-2)
       +(2*(4*n^5-18*n^4-23*n^3+266*n^2-523*n+330))*a(n-3)
       -(4*(n-2))*(n^2-4*n+5)*(2*n-5)^2*a(n-4))/
       ((n+1)*(n^2-6*n+10)))
    end:
seq(a(n), n=0..30);

Mathematica

Table[Sum[CatalanNumber[k]*(n - k)!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 13 2016 *)

Crossrefs

Cf. A000108, A000142, A277176, A277359, A277396.

Sequence in context: A284729 A006966 A336020 * A056841 A185040 A369599

Adjacent sequences: A277172 A277173 A277174 * A277176 A277177 A277178

Keyword

nonn

Author

Alois P. Heinz, Oct 02 2016

Status

approved