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A336171
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a(n) = Sum_{k=0..n} (-1)^(n-k) * (n+4*k)!/((n-k)! * k!^5).
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1
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1, 119, 112681, 166923119, 302857024681, 616967236620839, 1354737230950753441, 3135180238488702264959, 7543003841027749147438441, 18698821633118804601271092959, 47466852090165503045193665276041, 122841260732098480578334554450553679, 323029586700918689286922557725358306721
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OFFSET
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0,2
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COMMENTS
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Diagonal of the rational function 1 / (1 - Sum_{k=1..5} x_k + Product_{k=1..5} x_k).
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LINKS
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Table of n, a(n) for n=0..12.
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FORMULA
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G.f.: Sum_{k>=0} (5*k)!/k!^5 * x^k / (1+x)^(5*k+1).
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MATHEMATICA
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a[n_] := Sum[(-1)^(n - k)*(n + 4*k)!/((n - k)!*k!^5), {k, 0, n}]; Array[a, 13, 0] (* Amiram Eldar, Jul 10 2020 *)
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PROG
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(PARI) {a(n) = sum(k=0, n, (-1)^(n-k)*(n+4*k)!/((n-k)!*k!^5))}
(PARI) N=20; x='x+O('x^N); Vec(sum(k=0, N, (5*k)!/k!^5*x^k/(1+x)^(5*k+1)))
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CROSSREFS
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Column k=5 of A336169.
Cf. A082489.
Sequence in context: A192726 A266032 A269123 * A349429 A196429 A243779
Adjacent sequences: A336168 A336169 A336170 * A336172 A336173 A336174
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KEYWORD
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nonn
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AUTHOR
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Seiichi Manyama, Jul 10 2020
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STATUS
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approved
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