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A110197 Number triangle of sums of squared binomial coefficients. 1
1, 2, 1, 3, 5, 1, 4, 14, 10, 1, 5, 30, 46, 17, 1, 6, 55, 146, 117, 26, 1, 7, 91, 371, 517, 251, 37, 1, 8, 140, 812, 1742, 1476, 478, 50, 1, 9, 204, 1596, 4878, 6376, 3614, 834, 65, 1, 10, 285, 2892, 11934, 22252, 19490, 7890, 1361, 82, 1, 11, 385, 4917, 26334, 66352 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Alternatively, number square T(n,k) = Sum_{i=0..n} binomial(i+k,k)^2 read by antidiagonals. Columns include A000027, A000330, A024166, A086020, A086023, A086025. Row sums are A006134. Diagonal sums are A110198.

LINKS

Table of n, a(n) for n=0..59.

FORMULA

Number triangle T(n,k) = Sum_{i=0..n-k} binomial(i+k,k)^2.

EXAMPLE

Rows start

  1;

  2,   1;

  3,   5,   1;

  4,  14,  10,   1;

  5,  30,  46,  17,   1;

  6,  55, 146, 117,  26,   1;

PROG

(PARI) T(n, k) = sum(i=0, n-k, binomial(i+k, k)^2);

tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", ")); print(); ); \\ Michel Marcus, Dec 03 2016

CROSSREFS

Sequence in context: A104029 A208752 A119308 * A124819 A124019 A337886

Adjacent sequences:  A110194 A110195 A110196 * A110198 A110199 A110200

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Jul 15 2005

STATUS

approved

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Last modified September 27 08:39 EDT 2021. Contains 347689 sequences. (Running on oeis4.)