A060075 Third column of triangle A060074.

1, 14, 331, 12284, 663061, 49164554, 4798037791, 596372040824, 91991577140521, 17244625801225094, 3861296322290987251, 1017889493782391701364, 312043142223584185393981, 110072908401904868672053634, 44269461921572566583027776711, 20136444961077089693182895665904

Offset: 0

Author

Wolfdieter Lang, Mar 16 2001

Keywords

• nonn
• easy

Comments

Also third diagonal of triangle A060058.

a(n) is n-fold iterated sum of squares with last upper summation index 3 and other upper summation indices j[k]+1, k=2,...,n. See Comments A060061 for the threefold iteration with last upper summation index n.

Crossrefs

Cf. A000364, A060058, A060061, A060074.

Programs

Mathematica

a[n_] := (Abs[EulerE[2*n+2]] - Abs[EulerE[2*n]]) / 4; Array[a, 16] (* Amiram Eldar, May 03 2025 *)

PARI

a(n) = (abs(eulerfrac(2*n+2)) - abs(eulerfrac(2*n))) / 4; \\ Amiram Eldar, May 03 2025

Formula

a(n) = A060074(n+2, 2) = A060058(2+n, n).

a(n) = (1/4)*(A000364(n+1) - A000364(n)). - Benoit Cloitre, Apr 06 2003

G.f.: sin(x)^2/cos(x)^3 = x^2/2! + 14*x^4/4! + 331*x^6/6! + ... - Peter Bala, Oct 22 2019