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A026956
Self-convolution of array T given by A026615.
16
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
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)
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
KEYWORD
nonn
EXTENSIONS
More terms from Sean A. Irvine, Oct 20 2019
STATUS
approved