A227094 Binomial transform of A013999.

1, 2, 5, 18, 91, 574, 4199, 34650, 318645, 3237034, 36041657, 436713506, 5722676895, 80654047942, 1216703923147, 19562850695690, 333991034593833, 6034449711055890, 115036771019660269, 2307582082535387570, 48588759062255598563, 1071533741191907032590

Offset: 0

Author

Emanuele Munarini, Jul 01 2013

Keywords

• nonn

Crossrefs

Cf. A013999.

Programs

Maple

a:= proc(n) option remember; `if`(n<4, [1, 2, 5, 18][n+1],
      (n+6)*a(n-1)-(5*n+7)*a(n-2)+(8*n-7)*a(n-3)-(4*n-12)*a(n-4))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Jul 01 2013

Mathematica

a[n_] := a[n] = If[n < 4, {1, 2, 5, 18}[[n + 1]], (n + 6)*a[n - 1] - (5*n + 7)*a[n - 2] + (8*n - 7)*a[n - 3] - (4*n - 12)*a[n - 4]];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jun 04 2018, from Maple *)

Maxima

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

Formula

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

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

a(n) ~ n * n!. - Vaclav Kotesovec, Nov 02 2023