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 A336170 a(n) = Sum_{k=0..n} (-1)^(n-k) * (n+3*k)!/((n-k)! * k!^4). 2
 1, 23, 2401, 347279, 58370761, 10693893503, 2071837562929, 417449585719343, 86587926575712937, 18366152017597820303, 3965385492963153556441, 868598410928920193676023, 192552082030654661729957401, 43117650276328970463683450639, 9738695910884616220689842598481 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Diagonal of the rational function 1 / (1 - Sum_{k=1..4} x_k + Product_{k=1..4} x_k). LINKS Seiichi Manyama, Table of n, a(n) for n = 0..418 FORMULA G.f.: Sum_{k>=0} (4*k)!/k!^4 * x^k / (1+x)^(4*k+1). MATHEMATICA 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 *) PROG (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))) CROSSREFS Column k=4 of A336169. Cf. A082488. Sequence in context: A281787 A132937 A068655 * A232362 A233226 A233446 Adjacent sequences: A336167 A336168 A336169 * A336171 A336172 A336173 KEYWORD nonn AUTHOR Seiichi Manyama, Jul 10 2020 STATUS approved

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Last modified March 26 23:26 EDT 2023. Contains 361553 sequences. (Running on oeis4.)