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

0,2

Links

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

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)

a(n) ~ 49 * 4^(n-2) / sqrt(Pi*n). - Amiram Eldar, Oct 18 2025

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 *)

Prog

(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
(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

Crossrefs

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

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

Cf. A026959, A026960.

Sequence in context: A387619 A054665 A134963 * A026986 A181290 A026996

Adjacent sequences: A026953 A026954 A026955 * A026957 A026958 A026959

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 20 2019

Status

approved