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 A227096 Self-convolution of A013999. 1
 1, 2, 5, 20, 104, 632, 4396, 34680, 307236, 3026472, 32849364, 389704800, 5017492320, 69678231552, 1038078389376, 16513758904320, 279354776803200, 5007072973075200, 94783054774919040, 1889504358498754560, 39565281716813111040, 868194780280625779200 (list; graph; refs; listen; history; text; internal format)
 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: A006924 A212580 A261779 * A152562 A006867 A170946 Adjacent sequences: A227093 A227094 A227095 * A227097 A227098 A227099 KEYWORD nonn AUTHOR Emanuele Munarini, Jul 01 2013 STATUS approved

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Last modified May 29 22:39 EDT 2023. Contains 363044 sequences. (Running on oeis4.)