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A306409
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a(n) = -Sum_{0<=i<j<=n} (-1)^(i+j) * (i+j)!/(i!*j!).
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3
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0, 1, 3, 10, 34, 120, 434, 1597, 5949, 22363, 84655, 322245, 1232205, 4729453, 18210279, 70307546, 272087770, 1055139408, 4099200524, 15951053566, 62159391150, 242542955378, 947504851414, 3705431067156, 14505084243860, 56831711106496, 222853334131080
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: ( 1/(sqrt(1-4*x) * (1-x)) ) * ( x *c(x)/(1 + x *c(x)) ), where c(x) is the g.f. of A000108. - Seiichi Manyama, Jan 30 2023
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EXAMPLE
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--+------+---------+---------+---------
0 | 0 | 1 | 1 | 1
1 | 1 | 2 | 3 | 1
2 | 3 | 6 | 9 | 3
3 | 10 | 19 | 29 | 9
4 | 34 | 65 | 99 | 31
5 | 120 | 231 | 351 | 111
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MATHEMATICA
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Table[-Sum[Sum[(-1)^(i+j) * (i+j)!/(i!*j!), {i, 0, j-1}], {j, 0, n}], {n, 0, 25}] (* Vaclav Kotesovec, Apr 05 2019 *)
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PROG
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(PARI) a(n) = -sum(i=0, n, sum(j=i+1, n, (-1)^(i+j)*(i+j)!/(i!*j!)));
(PARI) my(N=30, x='x+O('x^N)); concat(0, Vec((1-sqrt(1-4*x))/(sqrt(1-4*x)*(1-x)*(3-sqrt(1-4*x))))) \\ Seiichi Manyama, Jan 30 2023
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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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