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

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

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.

Crossrefs

Cf. A000108, A045894, A035324.

Programs

Mathematica

Array[(#^2 + 27 # + 122) Binomial[2 (# + 5), # + 5]/24 - 5 (# + 8)*2^(2 # + 5) &, 20, 0] (* Michael De Vlieger, Sep 04 2018 *)

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.