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 A352471 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n,2*k+1)^3 * a(n-2*k-1). 2
 1, 1, 8, 217, 13952, 1752001, 380168432, 130996038265, 67377689108480, 49343690620021249, 49570079811804165008, 66280482720537078211945, 115058150837606807142692096, 253942526419333142443328522689, 700015299612132412448976873339008 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..14. FORMULA Sum_{n>=0} a(n) * x^n / n!^3 = 1 / (1 - Sum_{n>=0} x^(2*n+1) / (2*n+1)!^3). MATHEMATICA a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 2 k + 1]^3 a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 14}] nmax = 14; CoefficientList[Series[1/(1 - Sum[x^(2 k + 1)/(2 k + 1)!^3, {k, 0, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!^3 CROSSREFS Cf. A006154, A336195, A352468, A352470. Sequence in context: A247539 A188680 A329304 * A232157 A305517 A298964 Adjacent sequences: A352468 A352469 A352470 * A352472 A352473 A352474 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Mar 17 2022 STATUS approved

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Last modified July 13 09:13 EDT 2024. Contains 374274 sequences. (Running on oeis4.)