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 A073394 Seventh convolution of A002605(n) (generalized (2,2)-Fibonacci), n >= 0, with itself. 3
 1, 16, 160, 1248, 8304, 49344, 269184, 1372800, 6628512, 30584576, 135804416, 583471616, 2436145920, 9919484928, 39503038464, 154230921216, 591550292736, 2232748892160, 8305370185728, 30486351396864, 110551407403008, 396424924397568, 1406924861276160, 4945692873129984, 17231635316293632 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (16,-96,224,112,-1344,896,3712,-3168,-7424,3584,10752,1792,-7168,-6144,-2048,-256). FORMULA a(n) = Sum_{k=0..n} b(k)*c(n-k) with b(k) = A002605(k) and c(k) = A073393(k). a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+7, 7)*binomial(n-k, k)*2^(n-k). a(n) = ((2322320 + 2869040*n + 1379232*n^2 + 332247*n^3 + 42533*n^4 + 2757*n^5 + 71*n^6)*(n+1)*U(n+1) + 4*(235900 + 375554*n + 207009*n^2 + 54174*n^3 + 7318*n^4 + 492*n^5 + 13*n^6)*(n+2)*U(n))/(2^8*3^6*5*7), with U(n) = A002605(n), n >= 0. G.f.: 1/(1-2*x*(1+x))^8. EXAMPLE G.f. = 1 + 16*x + 160*x^2 + 1248*x^3 + ... + 154230921216*x^15 + 591550292736*x^16 + 2232748892160*x^17 + 8305370185728*x^18 + ... - Zerinvary Lajos, Jun 03 2009 MATHEMATICA CoefficientList[Series[1/(1-2*x-2*x^2)^8, {x, 0, 30}], x] (* G. C. Greubel, Oct 06 2022 *) LinearRecurrence[{16, -96, 224, 112, -1344, 896, 3712, -3168, -7424, 3584, 10752, 1792, -7168, -6144, -2048, -256}, {1, 16, 160, 1248, 8304, 49344, 269184, 1372800, 6628512, 30584576, 135804416, 583471616, 2436145920, 9919484928, 39503038464, 154230921216}, 30] (* Harvey P. Dale, Nov 21 2023 *) PROG (SageMath) taylor( 1/(1-2*x-2*x^2)^8, x, 0, 26).list() # Zerinvary Lajos, Jun 03 2009; modified by G. C. Greubel, Oct 06 2022 (Magma) R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/(1-2*x-2*x^2)^8 )); // G. C. Greubel, Oct 06 2022 CROSSREFS Eighth (m=7) column of triangle A073387. Cf. A002605, A073393. Sequence in context: A144453 A121036 A224058 * A038846 A079767 A079768 Adjacent sequences: A073391 A073392 A073393 * A073395 A073396 A073397 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Aug 02 2002 EXTENSIONS Terms a(19) onward added by G. C. Greubel, Oct 06 2022 STATUS approved

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Last modified August 11 19:17 EDT 2024. Contains 375073 sequences. (Running on oeis4.)