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 A306409 a(n) = -Sum_{0<=i
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1664 FORMULA a(n) = A006134(n) - A307354(n). a(n) = (A006134(n) - A120305(n))/2. a(n) ~ 4^(n+1) / (9*sqrt(Pi*n)). - Vaclav Kotesovec, Apr 05 2019 EXAMPLE n | a(n) | A307354 | A006134 | A120305 --+------+---------+---------+--------- 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 MATHEMATICA 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 *) PROG (PARI) {a(n) = -sum(i=0, n, sum(j=i+1, n, (-1)^(i+j)*(i+j)!/(i!*j!)))} CROSSREFS Cf. A006134, A057552, A120305, A307354. Sequence in context: A188622 A047017 A026616 * A047032 A149032 A149033 Adjacent sequences: A306406 A306407 A306408 * A306410 A306411 A306412 KEYWORD nonn AUTHOR Seiichi Manyama, Apr 05 2019 STATUS approved

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Last modified November 30 04:37 EST 2022. Contains 358431 sequences. (Running on oeis4.)