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A336170
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a(n) = Sum_{k=0..n} (-1)^(n-k) * (n+3*k)!/((n-k)! * k!^4).
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2
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1, 23, 2401, 347279, 58370761, 10693893503, 2071837562929, 417449585719343, 86587926575712937, 18366152017597820303, 3965385492963153556441, 868598410928920193676023, 192552082030654661729957401, 43117650276328970463683450639, 9738695910884616220689842598481
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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..4} x_k + Product_{k=1..4} x_k).
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..418
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FORMULA
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G.f.: Sum_{k>=0} (4*k)!/k!^4 * x^k / (1+x)^(4*k+1).
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MATHEMATICA
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a[n_] := Sum[(-1)^(n - k)*(n + 3*k)!/((n - k)!*k!^4), {k, 0, n}]; Array[a, 15, 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+3*k)!/((n-k)!*k!^4))}
(PARI) N=20; x='x+O('x^N); Vec(sum(k=0, N, (4*k)!/k!^4*x^k/(1+x)^(4*k+1)))
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CROSSREFS
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Column k=4 of A336169.
Cf. A082488.
Sequence in context: A281787 A132937 A068655 * A232362 A233226 A233446
Adjacent sequences: A336167 A336168 A336169 * A336171 A336172 A336173
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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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