A257142 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.

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

Offset

1,2

Comments

First column is A001906.

Links

Table of n, a(n) for n=1..45.

Formula

G.f.: N(x/(1-x)^2,y), where N(x,y) is the g.f. of Narayana's triangle A001263.

Example

1;
3,1;
8,7,1;
21,34,12,1;
55,141,89,18,1;
144,534,522,186,25,1;

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A001263, A001906.

Sequence in context: A005295 A077897 A308737 * A270861 A208656 A242440

Adjacent sequences: A257139 A257140 A257141 * A257143 A257144 A257145

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Apr 16 2015

Status

approved