A026956 Self-convolution of array T given by A026615.

1, 2, 11, 52, 200, 742, 2752, 10278, 38670, 146426, 557408, 2131318, 8179646, 31491202, 121568150, 470404274, 1823968074, 7085220834, 27567196704, 107414120214, 419080195374, 1636990646274, 6401210885934, 25055584929954, 98160790785714, 384885441746202, 1510279309724502

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000108, A026615, A026616, A026617, A026618, A026619, A026620.

Cf. A026621, A026622, A026623, A026624, A026625, A026957, A026958.

Cf. A026959, A026960.

Programs

Magma

[n le 1 select n+1 else Catalan(n-2)*(49*n^2-105*n+48)/n - 6: n in [0..40]]; // G. C. Greubel, Jun 17 2024

Mathematica

Table[If[n==0, 1, CatalanNumber[n-2]*(49*n^2-105*n+48)/n -6], {n,0,40}] (* G. C. Greubel, Jun 17 2024 *)

SageMath

[1,2]+[catalan_number(n-2)*(49*n^2-105*n+48)/n -6 for n in range(2,41)] # G. C. Greubel, Jun 17 2024

Formula

From G. C. Greubel, Jun 17 2024: (Start)

a(n) = Sum_{k=0..n} A026615(n, k) * A026615(n, n-k).

a(n) = A000108(n-2)*(49*n^2 - 105*n + 48)/n - 6, for n >= 1, with a(0) = 1.

G.f.: (4 - 8*x + 5*x^2 - x^3 - (3 - x + 4*x^2)*sqrt(1-4*x))/((1-x)*sqrt(1-4*x)).

E.g.f.: (1/6)*( 18 + 24*x - 36*exp(x) + 4*exp(2*x)*(6 - 6*x + x^2) * BesselI(0, 2*x) + x*exp(2*x)*(23 - 4*x)*BesselI(1, 2*x) ). (End)

Extensions

More terms from Sean A. Irvine, Oct 20 2019