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A227096
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Self-convolution of A013999.
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1
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1, 2, 5, 20, 104, 632, 4396, 34680, 307236, 3026472, 32849364, 389704800, 5017492320, 69678231552, 1038078389376, 16513758904320, 279354776803200, 5007072973075200, 94783054774919040, 1889504358498754560, 39565281716813111040, 868194780280625779200
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listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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FORMULA
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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).
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MAPLE
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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:
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MATHEMATICA
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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}];
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PROG
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(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);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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