

A188513


Riordan matrix (1/(x+sqrt(14x)),(1sqrt(14x))/(2(x+sqrt(14x))).


1



1, 1, 1, 3, 3, 1, 9, 11, 5, 1, 29, 40, 23, 7, 1, 97, 147, 99, 39, 9, 1, 333, 544, 413, 194, 59, 11, 1, 1165, 2025, 1691, 907, 333, 83, 13, 1, 4135, 7575, 6842, 4078, 1725, 524, 111, 15, 1, 14845, 28455, 27464, 17856, 8453, 2979, 775, 143, 17, 1, 53791, 107277, 109631, 76718, 39851, 15804, 4797, 1094, 179, 19, 1
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OFFSET

0,4


COMMENTS

Triangle begins:
1
1, 1
3, 3, 1
9, 11, 5, 1
29, 40, 23, 7, 1
97, 147, 99, 39, 9, 1
333, 544, 413, 194, 59, 11, 1
1165, 2025, 1691, 907, 333, 83, 13, 1
4135, 7575, 6842, 4078, 1725, 524, 111, 15, 1
First column = sequence A081696
Row sums = sequence A101850


LINKS

Table of n, a(n) for n=0..65.


FORMULA

T(n,k) = [x^n] ((1sqrt(14*x))/(2*(x+sqrt(14*x)))^k/(x+sqrt(14*x)).
T(n,k) = [x^(nk)] (12*x)/((1x)^(n+1)*(1xx^2)^(k+1)).
T(n,k) = sum(binomial(i+k,k)*binomial(2*ni,n+k+i)*(2*k+3*i+1)/(n+k+i+1), i=0..floor((nk)/2)).


MATHEMATICA

Flatten[Table[Sum[Binomial[i+k, k]Binomial[2ni, n+k+i](2k+3i+1)/(n+k+i+1), {i, 0, Floor[(nk)/2]}], {n, 0, 10}, {k, 0, n}]]


PROG

(Maxima) create_list(sum(binomial(i+k, k)*binomial(2*ni, n+k+i)*(2*k+3*i+1)/(n+k+i+1), i, 0, floor((nk)/2)), n, 0, 10, k, 0, n);


CROSSREFS

Cf. A081696, A101850.
Sequence in context: A215120 A084145 A122919 * A216916 A157401 A143911
Adjacent sequences: A188510 A188511 A188512 * A188514 A188515 A188516


KEYWORD

nonn,easy,tabl


AUTHOR

Emanuele Munarini, Apr 02 2011


STATUS

approved



