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 A143690 a(n) = A007318 * [1, 6, 14, 9, 0, 0, 0, ...]. 5
 1, 7, 27, 70, 145, 261, 427, 652, 945, 1315, 1771, 2322, 2977, 3745, 4635, 5656, 6817, 8127, 9595, 11230, 13041, 15037, 17227, 19620, 22225, 25051, 28107, 31402, 34945, 38745, 42811, 47152, 51777, 56695, 61915, 67446, 73297, 79477, 85995, 92860 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of [1, 6, 14, 9, 0, 0, 0,...]. Row sums of triangle A033292. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA From R. J. Mathar, Aug 29 2008: (Start) G.f.: (1 +3*x +5*x^2)/(1-x)^4. a(n) = A002412(n+1) + 5*A000292(n-1). (End) a(n) = A000326(n+1) + (n+1)*A000326(n). - Bruno Berselli, Jun 07 2013 From G. C. Greubel, May 30 2021: (start) a(n) = (n+1)*(3*n^2 +2*n +2)/2. E.g.f.: (1/2)*(2 +12*x +14*x^2 +3*x^3)*exp(x). (End) EXAMPLE a(3) = 70 = (1, 3, 3, 1) dot (1, 6, 14, 9) = (1 + 18 + 42 + 9). a(3) = 70 = sum of row 3 terms of triangle A033292: (13 + 16 + 19, + 22). MATHEMATICA Table[(n+1)*(3*n^2+2*n+2)/2, {n, 0, 50}] (* G. C. Greubel, May 30 2021 *) PROG (Sage) [(n+1)*(3*n^2+2*n+2)/2 for n in (0..50)] # G. C. Greubel, May 30 2021 CROSSREFS Cf. A000292, A000326, A002412, A033292. Cf. A226449. [Bruno Berselli, Jun 09 2013] Sequence in context: A265900 A159065 A098931 * A007715 A161439 A039623 Adjacent sequences: A143687 A143688 A143689 * A143691 A143692 A143693 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Aug 29 2008 EXTENSIONS Extended beyond a(14) by R. J. Mathar, Aug 29 2008 STATUS approved

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Last modified December 2 17:19 EST 2023. Contains 367525 sequences. (Running on oeis4.)