cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A060075 Third column of triangle A060074.

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%I A060075 #21 May 03 2025 07:45:12
%S A060075 1,14,331,12284,663061,49164554,4798037791,596372040824,
%T A060075 91991577140521,17244625801225094,3861296322290987251,
%U A060075 1017889493782391701364,312043142223584185393981,110072908401904868672053634,44269461921572566583027776711,20136444961077089693182895665904
%N A060075 Third column of triangle A060074.
%C A060075 Also third diagonal of triangle A060058.
%C A060075 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.
%F A060075 a(n) = A060074(n+2, 2) = A060058(2+n, n).
%F A060075 a(n) = (1/4)*(A000364(n+1) - A000364(n)). - _Benoit Cloitre_, Apr 06 2003
%F A060075 G.f.: sin(x)^2/cos(x)^3 = x^2/2! + 14*x^4/4! + 331*x^6/6! + ... - _Peter Bala_, Oct 22 2019
%t A060075 a[n_] := (Abs[EulerE[2*n+2]] - Abs[EulerE[2*n]]) / 4; Array[a, 16] (* _Amiram Eldar_, May 03 2025 *)
%o A060075 (PARI) a(n) = (abs(eulerfrac(2*n+2)) - abs(eulerfrac(2*n))) / 4; \\ _Amiram Eldar_, May 03 2025
%Y A060075 Cf. A000364, A060058, A060061, A060074.
%K A060075 nonn,easy
%O A060075 0,2
%A A060075 _Wolfdieter Lang_, Mar 16 2001