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.
%I A136659 #15 Aug 31 2025 02:54:34
%S A136659 1,9,75,660,6300,65520,740880,9072000,119750400,1696464000,
%T A136659 25686460800,414096883200,7083236160000,128152088064000,
%U A136659 2445351068160000,49084865077248000,1033983353475072000,22808456326656000000,525810946517176320000,12645008187498086400000
%N A136659 Unsigned third column (k=2) of triangle A136656 divided by 4.
%C A136659 Also unsigned second column of triangle A136657 divided by 2.
%D A136659 Charalambos A. Charalambides, Enumerative Combinatorics, Chapman & Hall/CRC, Boca Raton, Florida, 2002, Table 8.3, p. 311, with s=-2, k=2 column/4.
%F A136659 a(n) = |A136656(n+2,2)|/4, n>=0.
%F A136659 E.g.f.: (2+6*x-3*x^2)/(2*(1-x)^6) (derived from the one given for the column k=2 under A136656).
%F A136659 a(n) = (n+4)!/2 * sum((k+1)!/(k+4)!,k=1..n), with offset 1. - _Gary Detlefs_, Jul 27 2010
%F A136659 a(n) = (1/48) * (n+8)*(n+1)*(n+3)!. - _Gary Detlefs_, Aug 03 2010
%F A136659 From _Amiram Eldar_, Aug 31 2025: (Start)
%F A136659 Sum_{n>=0} 1/a(n) = 44836/245 - 480*e/7 - 24*gamma/7 + 24*ExpIntegralEi(1)/7, where e = A001113, gamma = A001620, and ExpIntegralEi(1) = A091725.
%F A136659 Sum_{n>=0} (-1)^n/a(n) = 39724/245 - 3120/(7*e) + 24*gamma/7 - 24*ExpIntegralEi(-1)/7, where ExpIntegralEi(-1) = -A099285. (End)
%t A136659 a[n_] := (n + 8)*(n + 1)*(n + 3)!/48; Array[a, 20, 0] (* _Amiram Eldar_, Aug 31 2025 *)
%Y A136659 Cf. A001710 (1/2 of unsigned k=1 column of A136657). A136660 (k=3 column divided by 8), A136656.
%Y A136659 Cf. A001113, A001620, A091725, A099285.
%K A136659 nonn,easy,changed
%O A136659 0,2
%A A136659 _Wolfdieter Lang_, Feb 22 2008