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A001780 Expansion of 1/((1+x)(1-x)^9). 6
1, 8, 37, 128, 367, 920, 2083, 4352, 8518, 15792, 27966, 47616, 78354, 125136, 194634, 295680, 439791, 641784, 920491, 1299584, 1808521, 2483624, 3369301, 4519424, 5998876, 7885280, 10270924, 13264896 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Jia Huang, Partially Palindromic Compositions, J. Int. Seq. (2023) Vol. 26, Art. 23.4.1. See pp. 4, 17.
Index entries for linear recurrences with constant coefficients, signature (8,-27,48,-42,0,42,-48,27,-8,1).
FORMULA
a(n) = 431*n/168 + (-1)^n/512 + 391*n^3/288 + 26011*n^2/10080 + 797*n^4/1920 + 11*n^5/144 + n^6/120 + n^7/2016 + n^8/80640 + 511/512. - R. J. Mathar, Mar 15 2011
Boas-Buck recurrence: a(n) = (1/n)*Sum_{p=0..n-1} (9 + (-1)^(n-p))*a(p), n >= 1, a(0) = 1. See the Boas-Buck comment in A046521 (here for the unsigned column k = 4 with offset 0). - Wolfdieter Lang, Aug 10 2017
a(n)+a(n+1) = A000581(n+9) . - R. J. Mathar, Jan 06 2021
PROG
(PARI) Vec(1/(1+x)/(1-x)^9+O(x^99)) \\ Charles R Greathouse IV, Apr 18 2012
CROSSREFS
Cf. A001769, A158454 (signed column k=4), A001779 (first differences), A169796 (binomial trans.).
Sequence in context: A309281 A296537 A052387 * A258476 A320754 A053296
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified May 18 15:50 EDT 2024. Contains 372664 sequences. (Running on oeis4.)