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 A187004 Expansion of A(x) = (1 + 2*x^2 + 6*x^3 + 9*x^4 + 8*x^5 + 5*x^6) / (1 - x - 2*x^2 - 3*x^3 - 3*x^4 - 2*x^5 - x^6). 1
 1, 5, 16, 41, 101, 254, 638, 1609, 4048, 10185, 25631, 64502, 162319, 408476, 1027931, 2586793, 6509675, 16381622, 41224415, 103741401, 261065639, 656972695, 1653274340, 4160471302, 10469842201, 26347398589, 66303330946 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The value of a(0) is undefined. The A(x) leads to a(0)=1, the a(n) formula to a(0)=0 and the recurrence relation to a(0)=6 as pointed out by Bruno Berselli. - Johannes W. Meijer, Jul 10 2011 LINKS Ivan Panchenko, Table of n, a(n) for n = 1..200 Kruchinin Vladimir Victorovich, Composition of ordinary generating functions, arXiv:1009.2565 [math.CO], 2010. Index entries for linear recurrences with constant coefficients, signature (1, 2, 3, 3, 2, 1). FORMULA a(n) = n*Sum_{m=1..n} Sum_{k=m..n} binomial(m, k-m)*Sum_{j=0..k} binomial(k,j) * binomial(j, n-3*k+2*j)))/m). a(n) = a(n-1) + 2*a(n-2) + 3*a(n-3) + 3*a(n-4) + 2*a(n-5) + a(n-6); a(1)=1, a(2)=5, a(3)=16, a(4)=41, a(5)=101, a(6)=254. - Harvey P. Dale, Jun 14 2011 MAPLE A187004 := proc(n) local m, k, j: (n*add(add(binomial(m, k-m)*add(binomial(k, j)*binomial(j, n-3*k+2*j), j=0..k), k=m..n)/m, m= 1..n)) end: seq(A187004(n), n=1..27); # Johannes W. Meijer, Jul 10 2011 MATHEMATICA LinearRecurrence[{1, 2, 3, 3, 2, 1}, {1, 5, 16, 41, 101, 254}, 30] (* or *) Rest[ CoefficientList[Series[(1+2x^2+6x^3+9x^4+8x^5+5x^6)/(1-x-2x^2- 3x^3-3x^4-2x^5-x^6), {x, 1, 30}], x]] (* Harvey P. Dale, Jun 14 2011 *) PROG (Maxima) a(n):=n*sum(sum(binomial(m, k-m)*sum(binomial(k, j)*binomial(j, n-3*k+2*j), j, 0, k), k, m, n)/m, m, 1, n); CROSSREFS Sequence in context: A014171 A014175 A097810 * A255135 A055796 A002662 Adjacent sequences:  A187001 A187002 A187003 * A187005 A187006 A187007 KEYWORD nonn,easy AUTHOR Vladimir Kruchinin, Mar 01 2011 STATUS approved

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Last modified July 27 08:33 EDT 2021. Contains 346304 sequences. (Running on oeis4.)