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A035330 5-fold convolution of A001700(n), n >= 0. 3
1, 15, 140, 1045, 6835, 40963, 230720, 1240740, 6437890, 32468470, 160010280, 773624615, 3680728375, 17274086235, 80119845080, 367821324040, 1673528845710, 7554110698850, 33858536700040, 150802994850570 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Fifth column of triangular array A035324.
LINKS
José Agapito, Ângela Mestre, Maria M. Torres, and Pasquale Petrullo, On One-Parameter Catalan Arrays, Journal of Integer Sequences, Vol. 18 (2015), Article 15.5.1.
Milan Janjić, Pascal Matrices and Restricted Words, J. Int. Seq., Vol. 21 (2018), Article 18.5.2.
FORMULA
a(n) = (n^2+27*n+122)*binomial(2*(n+5), n+5)/24 - 5*(n+8)*2^(2*n+5) = A035324(n+5, 5);
G.f.: c(x)^5/(1-4*x)^(5/2), where c(x) = g.f. for Catalan numbers A000108.
MATHEMATICA
Array[(#^2 + 27 # + 122) Binomial[2 (# + 5), # + 5]/24 - 5 (# + 8)*2^(2 # + 5) &, 20, 0] (* Michael De Vlieger, Sep 04 2018 *)
CROSSREFS
Sequence in context: A027802 A302855 A133716 * A002803 A354394 A346977
KEYWORD
easy,nonn
AUTHOR
STATUS
approved

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Last modified February 26 13:34 EST 2024. Contains 370352 sequences. (Running on oeis4.)