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

0,2

Links

Table of n, a(n) for n=0..21.

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

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 *)

Prog

(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);

Crossrefs

Cf. A013999.

Sequence in context: A005500 A020025 A113715 * A173227 A099556 A057864

Adjacent sequences: A227091 A227092 A227093 * A227095 A227096 A227097

Keyword

nonn

Author

Emanuele Munarini, Jul 01 2013

Status

approved