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 A060058 Triangle of numbers related to A000330 (sum of squares) and A000364 (Euler numbers). 13
 1, 1, 1, 1, 5, 5, 1, 14, 61, 61, 1, 30, 331, 1385, 1385, 1, 55, 1211, 12284, 50521, 50521, 1, 91, 3486, 68060, 663061, 2702765, 2702765, 1, 140, 8526, 281210, 5162421, 49164554, 199360981, 199360981, 1, 204 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums give A060059. Columns give A000012 (powers of 1), A000330 (sum of squares), A060060-2 for m=0,...,4. Main diagonal gives Euler numbers A000364. See triangle A060074. LINKS W. Lang, First 9 rows. FORMULA a(n, m) = a(n-1, m)+((n+1-m)^2)*a(n, m-1), a(n, -1) := 0, a(0, 0)=1, a(n, m)=0 if n= m >= 0, with the rectangular array ay(n, m) := sum((j^2)*ay(j+1, m-1), j=1..n), n >= 0, m >= 1; input: ay(n, 0)=1 (iterated sums of squares). G.f. for m-th column: 1/(1-x) for m=0, (x^m)*sum(A060063(m, k)*x^k, k=0..m)/(1-x)^(3*m+1), m >= 1. Recursion for g.f.s for m-th column: (1-x)*G(m, x)= x*G''(m-1, x)- G'(m-1, x) + G(m-1, x)/x, m>=2; G(1, x)=x*(1+x)/(1-x)^4; the apostrophe denotes differentiation w.r.t. x. G(0, x)=1/(1-x). Wolfdieter Lang, Feb 13 2004. EXAMPLE {1}; {1,1}; {1,5,5,}; {1,14,61,61}; ... MATHEMATICA a[_, -1] = 0; a[0, 0] = 1; a[n_, m_] /; n < m = 0; a[n_, m_] := a[n, m] = a[n-1, m] + (n+1-m)^2*a[n, m-1]; Table[a[n, m], {n, 0, 8}, {m, 0, n}] // Flatten (* Jean-François Alcover, Jul 09 2013 *) CROSSREFS Sequence in context: A011094 A204005 A075298 * A092766 A288389 A060074 Adjacent sequences:  A060055 A060056 A060057 * A060059 A060060 A060061 KEYWORD nonn,easy,tabl AUTHOR Wolfdieter Lang, Mar 16 2001 STATUS approved

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Last modified August 18 00:28 EDT 2018. Contains 313817 sequences. (Running on oeis4.)