login
A371401
Triangle read by rows: T(n, k) = [x^k] (n*x + 1)*Hypergeometric([-n, -n + 1], [1], x).
1
1, 1, 1, 1, 4, 4, 1, 9, 21, 9, 1, 16, 66, 76, 16, 1, 25, 160, 340, 205, 25, 1, 36, 330, 1100, 1275, 456, 36, 1, 49, 609, 2905, 5425, 3801, 889, 49, 1, 64, 1036, 6664, 18130, 20776, 9604, 1576, 64, 1, 81, 1656, 13776, 51156, 86436, 65856, 21456, 2601, 81
OFFSET
0,5
FORMULA
Sum_{k=0..n} a(n) = (n + 1)*binomial(2*n - 1, n).
EXAMPLE
Triangle starts:
[0] 1;
[1] 1, 1;
[2] 1, 4, 4;
[3] 1, 9, 21, 9;
[4] 1, 16, 66, 76, 16;
[5] 1, 25, 160, 340, 205, 25;
[6] 1, 36, 330, 1100, 1275, 456, 36;
[7] 1, 49, 609, 2905, 5425, 3801, 889, 49;
[8] 1, 64, 1036, 6664, 18130, 20776, 9604, 1576, 64;
MAPLE
P := (n, x) -> (n*x + 1)*hypergeom([-n, -n + 1], [1], x):
T := (n, k) -> coeff(simplify(P(n, x)), x, k):
seq(seq(T(n, k), k = 0..n), n = 0..9);
CROSSREFS
Cf. A371400, A097070 (row sums, shifted).
Sequence in context: A358204 A138679 A179399 * A080721 A123588 A373504
KEYWORD
nonn,tabl,easy
AUTHOR
Peter Luschny, Mar 22 2024
STATUS
approved