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 A227094 Binomial transform of A013999. 0
 1, 2, 5, 18, 91, 574, 4199, 34650, 318645, 3237034, 36041657, 436713506, 5722676895, 80654047942, 1216703923147, 19562850695690, 333991034593833, 6034449711055890, 115036771019660269, 2307582082535387570, 48588759062255598563, 1071533741191907032590 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS 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). 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

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Last modified September 20 07:21 EDT 2020. Contains 337264 sequences. (Running on oeis4.)