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 A084851 Binomial transform of binomial(n+2,2). 5
 1, 4, 13, 38, 104, 272, 688, 1696, 4096, 9728, 22784, 52736, 120832, 274432, 618496, 1384448, 3080192, 6815744, 15007744, 32899072, 71827456, 156237824, 338690048, 731906048, 1577058304, 3388997632, 7264534528, 15535702016, 33151778816 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Essentially the same as A049611. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Igor Makhlin, GrÃ¶bner fans of Hibi ideals, generalized Hibi ideals and flag varieties, arXiv:2003.02916 [math.CO], 2020. Index entries for linear recurrences with constant coefficients, signature (6,-12,8). FORMULA G.f.: (1 - x)^2/(1 - 2*x)^3. a(n) = (n^2 + 7*n + 8)*2^(n - 3). a(n) = Sum_{k=0..n} C(n, k)*C(k+2, 2). a(n) = A049611(n+1). EXAMPLE From Bruno Berselli, Jul 17 2018: (Start) Let the triangle:    1    3,  4    6,  9,  13   10, 16,  25,  38   15, 25,  41,  66, 104   21, 36,  61, 102, 168, 272   28, 49,  85, 146, 248, 416,  688   36, 64, 113, 198, 344, 592, 1008, 1696, etc. where the first column is A000217 (without 0). The other terms are calculated with the recurrence T(r, c) = T(r-1, c-1) + T(r, c-1). The sequence is the right side of the triangle. (End) MAPLE a := n -> hypergeom([-n, 3], [1], -1); seq(round(evalf(a(n), 32)), n=0..31); # Peter Luschny, Aug 02 2014 MATHEMATICA CoefficientList[ Series[(1 - x)^2/(1 - 2 x)^3, {x, 0, 28}], x] (* Robert G. Wilson v, Jun 28 2005 *) LinearRecurrence[{6, -12, 8}, {1, 4, 13}, 30] (* Harvey P. Dale, Aug 05 2019 *) PROG (MAGMA) [(n^2+7*n+8)*2^(n-3): n in [0..40]]; // Vincenzo Librandi, Aug 03 2014 CROSSREFS Cf. A000217, A049611, A058396 (first differences). Sequence in context: A089092 A181527 A049611 * A094706 A325927 A056014 Adjacent sequences:  A084848 A084849 A084850 * A084852 A084853 A084854 KEYWORD nonn,easy AUTHOR Paul Barry, Jun 09 2003 STATUS approved

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Last modified May 11 21:35 EDT 2021. Contains 343808 sequences. (Running on oeis4.)