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A277175 Convolution of Catalan numbers and factorial numbers. 4
1, 2, 5, 15, 53, 222, 1120, 6849, 50111, 427510, 4142900, 44693782, 529276962, 6813205468, 94642629984, 1410507388421, 22445134308123, 379776665469030, 6808016435182620, 128886547350655050, 2569493300908367550, 53805226930896987540, 1180673761078007109840 (list; graph; refs; listen; history; text; internal format)
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: A022493 A284729 A006966 * A056841 A185040 A208237

Adjacent sequences:  A277172 A277173 A277174 * A277176 A277177 A277178

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 02 2016

STATUS

approved

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Last modified March 19 23:02 EDT 2019. Contains 321343 sequences. (Running on oeis4.)