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A257142
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Triangle read by rows: T(n,m) = Sum_{k=0..n} C(k-1,m-1)*C(k,m-1)*C(n+k-1,n-k)/m.
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0
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1, 3, 1, 8, 7, 1, 21, 34, 12, 1, 55, 141, 89, 18, 1, 144, 534, 522, 186, 25, 1, 377, 1905, 2651, 1445, 340, 33, 1, 987, 6512, 12198, 9370, 3350, 568, 42, 1, 2584, 21557, 52211, 53533, 26804, 6881, 889, 52, 1
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: N(x/(1-x)^2,y), where N(x,y) is the g.f. of Narayana's triangle A001263.
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EXAMPLE
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1;
3,1;
8,7,1;
21,34,12,1;
55,141,89,18,1;
144,534,522,186,25,1;
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MATHEMATICA
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Table[Sum[Binomial[k - 1, m - 1] * Binomial[k, m - 1] * Binomial[n + k - 1, n - k]/m, {k, 0, n}], {n, 9}, {m, n}] // Flatten (* Michael De Vlieger, Apr 17 2015 *)
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PROG
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(Maxima) T(n, m):=sum(binomial(k-1, m-1)*binomial(k, m-1)*binomial(n+k-1, n-k)/m, k, 0, n);
(PARI) tabl(nn) = {default(seriesprecision, nn+1); pol = subst((1-xx*(1+y)-sqrt((1-xx*(1+y))^2-4*y*xx^2))/(2*xx), xx, x/(1-x)^2) + O(x^nn); for (n=1, nn-1, poly = polcoeff(pol, n, x); for (k=1, n, print1(polcoeff(poly, k, y), ", "); ); print(); ); } \\ Michel Marcus, Apr 17 2015
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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