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 A144661 a(n) = Sum_{i=0..n} Sum_{j=0..n} Sum_{k=0..n} Sum_{l=0..n} (i+j+k+l)!/(i!*j!*k!*l!). 5
 1, 65, 7365, 1107697, 191448941, 35899051101, 7101534312685, 1458965717496881, 308290573348183629, 66577182435768923245, 14629025943480502591445, 3260160391173522631759533, 735119604833362632050789701, 167408468505328518543519208949, 38448088693846486556578015883325 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..400 (terms 0..50 from Seiichi Manyama) Vaclav Kotesovec, Recurrence (of order 4) Vidunas, Raimundas Counting derangements and Nash equilibria Ann. Comb. 21, No. 1, 131-152 (2017). FORMULA a(n) ~ 2^(8*n + 15/2) / (81 * Pi^(3/2) * n^(3/2)). - Vaclav Kotesovec, Apr 02 2019 MAPLE f:=n->add( add( add( add( (i+j+k+l)!/(i!*j!*k!*l!), i=0..n), j=0..n), k=0..n), l=0..n); [seq(f(n), n=0..20)]; MATHEMATICA Table[Sum[(i + j + k + l)! / (i!*j!*k!*l!), {i, 0, n}, {j, 0, n}, {k, 0, n}, {l, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 02 2019 *) Table[Sum[(1 + j + k + l + n)!/((1 + j + k + l)*j!*k!*l!), {j, 0, n}, {k, 0, n}, {l, 0, n}] / n!, {n, 0, 20}] (* Vaclav Kotesovec, Apr 03 2019 *) Table[Sum[(1 + k + l + 2*n)! * HypergeometricPFQ[{1, -1 - k - l - n, -n}, {-1 - k - l - 2*n, -k - l - n}, 1] / ((1 + k + l + n)*k!*l!*n!), {k, 0, n}, {l, 0, n}]/n!, {n, 0, 20}] (* Vaclav Kotesovec, Apr 03 2019 *) PROG (PARI) {a(n) = sum(i=0, n, sum(j=0, n, sum(k=0, n, sum(l=0, n, (i+j+k+l)!/(i!*j!*k!*l!)))))} \\ Seiichi Manyama, Apr 02 2019 CROSSREFS Cf. A030662, A144660, A144662, A307324. Sequence in context: A116121 A118707 A282839 * A296144 A251150 A176370 Adjacent sequences: A144658 A144659 A144660 * A144662 A144663 A144664 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 01 2009 STATUS approved

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Last modified April 12 17:42 EDT 2024. Contains 371635 sequences. (Running on oeis4.)