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 A062750 Generalized Catalan array FS(4; n,r). 4
 1, 1, 1, 1, 1, 1, 2, 3, 4, 4, 4, 4, 1, 3, 6, 10, 14, 18, 22, 22, 22, 22, 1, 4, 10, 20, 34, 52, 74, 96, 118, 140, 140, 140, 140, 1, 5, 15, 35, 69, 121, 195, 291, 409, 549, 689, 829, 969, 969, 969, 969, 1, 6, 21, 56, 125 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS In the Frey-Sellers reference this array is called {n over r}_{m-1}, with m=4. The step width sequence of this staircase array is [1,3,3,3,....], i.e. the degree of the row polynomials is [0,3,6,9,...]= A008585. The columns r=0..6 give A000012 (powers of 1), A000027 (natural), A000217 (triangular), A000292 (tetrahedral), A063258, A027659, A062966. LINKS D. D. Frey and J. A. Sellers, Generalizing Bailey's generalization of the Catalan numbers, The Fibonacci Quarterly, 39 (2001) 142-148. FORMULA a(0, 0)=1, a(n, -1)=0, n >= 1; a(n, r)=0 if r>3*n; a(n, r)=a(n, r-1)+a(n-1, r) else. G.f. for column r=3*k+j, k >= 0, j=1, 2, 3: (x^(k+1))*N(4; k, x)/(1-x)^(3*k+1+j), with the row polynomials N(4; k, x) of array A062751. EXAMPLE {1}; {1,1,1,1}; {1,2,3,4,4,4,4}; {1,3,6,10,14,18,22,22,22,22}; ...; N(4; 1,x)=(2-x)*(2-2*x+x^2). CROSSREFS Sequence in context: A171502 A005102 A030241 * A193669 A065686 A158411 Adjacent sequences:  A062747 A062748 A062749 * A062751 A062752 A062753 KEYWORD nonn,easy,tabf AUTHOR Wolfdieter Lang, Jul 12 2001 STATUS approved

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Last modified October 23 03:21 EDT 2019. Contains 328335 sequences. (Running on oeis4.)