A227096 Self-convolution of A013999.

1, 2, 5, 20, 104, 632, 4396, 34680, 307236, 3026472, 32849364, 389704800, 5017492320, 69678231552, 1038078389376, 16513758904320, 279354776803200, 5007072973075200, 94783054774919040, 1889504358498754560, 39565281716813111040, 868194780280625779200

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) = sum(A013999(k)*A013999(n-k), k=0..n).

G.f.: sum(B(k)*k!*x^(k-2)*(1-x)^k, k>=2), where B(k) = sum(1/C(k,i), i=1..k-1).

a(n) ~ 2*n*n!/exp(1). - Vaclav Kotesovec, Jul 08 2013

Maple

a:= proc(n) option remember; `if`(n<6, [1, 2, 5, 20, 104, 632][n+1],
      ((3*n+10)*(n+3)*a(n-1) -(n+13)*(n+2)^2*a(n-2)
       +(n+3)*(4*n^2+19*n+2)*a(n-3) -2*(n+2)*(3*n^2+6*n-4)*a(n-4)
       +(4*n^3+8*n^2-12*n-4)*a(n-5) -n*(n+3)*(n-2)*a(n-6))/(2*n+4))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Jul 01 2013

Mathematica

f[n_] := Sum[Binomial[n-k+1, k] (-1)^k (n-k+1)!, {k, 0, Quotient[n+1, 2]}];
a[n_] := Sum[f[k] f[n-k], {k, 0, n}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 14 2023 *)

Prog

(Maxima) f(n):=sum(binomial(n-k+1, k)*(-1)^k*(n-k+1)!, k, 0, floor((n+1)/2)); a(n):=sum(f(k)*f(n-k), k, 0, n); makelist(a(n), n, 0, 20);

Crossrefs

Cf. A013999.

Sequence in context: A212580 A370669 A261779 * A152562 A006867 A170946

Adjacent sequences: A227093 A227094 A227095 * A227097 A227098 A227099

Keyword

nonn

Author

Emanuele Munarini, Jul 01 2013

Status

approved