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 A119363 a(n) = Sum_{k=0..n} C(n,3k)^2. 7
 1, 1, 1, 2, 17, 101, 402, 1275, 3921, 14114, 58601, 243695, 950578, 3537847, 13166791, 50514102, 198627921, 782913717, 3054480306, 11824753551, 45823049817, 178682390994, 700285942731, 2747647985241, 10767833451954, 42164261091351, 165225573240651 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS a(n) - A119364(n) = A119365(n). LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 FORMULA From Vaclav Kotesovec, Mar 12 2019: (Start) Recurrence: (n-2)*(n-1)*n*(637*n^6 - 11466*n^5 + 84364*n^4 - 324394*n^3 + 686227*n^2 - 755060*n + 336132)*a(n) = 3*(n-2)*(n-1)*(1274*n^7 - 23569*n^6 + 180194*n^5 - 733383*n^4 + 1699606*n^3 - 2208294*n^2 + 1449504*n - 351000)*a(n-1) - 3*(n-2)*(3185*n^8 - 63700*n^7 + 539028*n^6 - 2512118*n^5 + 7020469*n^4 - 11971242*n^3 + 12050010*n^2 - 6446736*n + 1362744)*a(n-2) + (14014*n^9 - 315315*n^8 + 3072678*n^7 - 16986046*n^6 + 58535088*n^5 - 129861691*n^4 + 184326992*n^3 - 159830656*n^2 + 75517728*n - 14313456)*a(n-3) + 3*(n-3)*(3185*n^8 - 63700*n^7 + 538391*n^6 - 2501394*n^5 + 6946794*n^4 - 11707256*n^3 + 11530544*n^2 - 5915328*n + 1142208)*a(n-4) + 18*(n-4)*(n-3)*(2*n - 9)*(637*n^6 - 7644*n^5 + 36589*n^4 - 88858*n^3 + 114124*n^2 - 71840*n + 16440)*a(n-5). a(n) ~ 4^n / (3*sqrt(Pi*n)). (End) MATHEMATICA Table[Sum[Binomial[n, 3k]^2, {k, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Mar 12 2019 *) Table[HypergeometricPFQ[{1/3 - n/3, 1/3 - n/3, 2/3 - n/3, 2/3 - n/3, -n/3, -n/3}, {1/3, 1/3, 2/3, 2/3, 1}, 1], {n, 0, 30}] (* Vaclav Kotesovec, Mar 12 2019 *) CROSSREFS Central coefficients of number triangle A119335. a(n) = A119335(2n, n). Cf. A024493, A119358, A139468, A139469. Sequence in context: A127533 A023260 A174365 * A272065 A129977 A213787 Adjacent sequences: A119360 A119361 A119362 * A119364 A119365 A119366 KEYWORD easy,nonn AUTHOR Paul Barry, May 16 2006 EXTENSIONS Edited by N. J. A. Sloane, Jun 12 2008 STATUS approved

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Last modified August 7 15:35 EDT 2024. Contains 375017 sequences. (Running on oeis4.)