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A035330

5-fold convolution of A001700(n), n >= 0.

1, 15, 140, 1045, 6835, 40963, 230720, 1240740, 6437890, 32468470, 160010280, 773624615, 3680728375, 17274086235, 80119845080, 367821324040, 1673528845710, 7554110698850, 33858536700040, 150802994850570

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OFFSET

0,2

COMMENTS

Fifth column of triangular array A035324.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..1650

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

Cf. A000108, A045894, A035324.

Sequence in context: A027802 A302855 A133716 * A002803 A354394 A346977

Adjacent sequences: A035327 A035328 A035329 * A035331 A035332 A035333

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved