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 A049128 Revert transform of x*(x - 1)^2/(1 - x + x^3). 6
 1, 1, 2, 6, 20, 70, 255, 959, 3696, 14520, 57930, 234080, 955999, 3939949, 16364985, 68437033, 287910048, 1217627176, 5173854018, 22077273858, 94564541166, 406451008386, 1752472631360, 7577758539846, 32852955892191 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 Index entries for reversions of series FORMULA a(n) = 1/n*(Sum_{l=1..n} C(n,l)*Sum_{i=1..n-1} C(i-1,i-2*l)*C(n-l,n-i-1)) + 1. - Vladimir Kruchinin, Jun 26 2015 D-finite with recurrence 2*n*(2*n-1) *a(n) +(-31*n^2+62*n-30) *a(n-1) +3*(20*n^2-54*n+25) *a(n-2) +(10*n^2-350*n+1023) *a(n-3) +(-124*n^2+1256*n-3063) *a(n-4) +(n-5) *(173*n-951)*a(n-5) -92*(n-5)*(n-6)*a(n-6)=0. - R. J. Mathar, Jul 20 2023 MAPLE a:= proc(n) option remember; `if`(n<5, [1, 1, 2, 6][n], ((1404*n^4-9489*n^3+22155*n^2-21012*n+6840)*a(n-1) -(n-2)*(2548*n^3-14719*n^2+25575*n-12330)*a(n-2) +(n-2)*(n-3)*(2548*n^2-10663*n+7662)*a(n-3) -(23*(n-2))*(n-3)*(n-4)*(52*n-51)*a(n-4))/ ((2*(2*n-1))*n*(52*n-103)*(n-3))) end: seq(a(n), n=1..30); # Alois P. Heinz, Jun 26 2015 MATHEMATICA a[n_] := 1/n*(Sum[Binomial[n, l]*Sum[Binomial[i-1, i-2*l]*Binomial[n-l, n-i-1], {i, 1, n-1}], {l, 1, n}])+1; Array[a, 30] (* Jean-François Alcover, Apr 03 2017, after Vladimir Kruchinin *) PROG (Maxima) a(n):=1/n*(sum(binomial(n, l)*sum(binomial(i-1, i-2*l)*binomial(n-l, n-i-1), i, 1, n-1), l, 1, n))+1; /* Vladimir Kruchinin, Jun 26 2015 */ CROSSREFS Sequence in context: A049138 A095929 A078482 * A192540 A369630 A185202 Adjacent sequences: A049125 A049126 A049127 * A049129 A049130 A049131 KEYWORD nonn AUTHOR Olivier Gérard EXTENSIONS NAME multiplied by x. - R. J. Mathar, Jul 23 2023 STATUS approved

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Last modified August 14 06:31 EDT 2024. Contains 375146 sequences. (Running on oeis4.)