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A385343
Exponential Riordan array (1, arcsin(x)).
34
1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 4, 0, 1, 0, 9, 0, 10, 0, 1, 0, 0, 64, 0, 20, 0, 1, 0, 225, 0, 259, 0, 35, 0, 1, 0, 0, 2304, 0, 784, 0, 56, 0, 1, 0, 11025, 0, 12916, 0, 1974, 0, 84, 0, 1, 0, 0, 147456, 0, 52480, 0, 4368, 0, 120, 0, 1, 0, 893025, 0, 1057221, 0, 172810, 0, 8778, 0, 165, 0, 1
OFFSET
0,13
FORMULA
E.g.f. of column k (with leading zeros): arcsin(x)^k / k!
T(n,k) = A121408(n,k) for k > 0.
EXAMPLE
Triangle starts:
1;
0, 1;
0, 0, 1;
0, 1, 0, 1;
0, 0, 4, 0, 1;
0, 9, 0, 10, 0, 1;
0, 0, 64, 0, 20, 0, 1;
0, 225, 0, 259, 0, 35, 0, 1;
PROG
(PARI) T(n, k) = my(x='x+O('x^(n+1))); n!*polcoef(asin(x)^k/k!, n);
CROSSREFS
Essentialy same as A121408.
Row sums give A006228.
Sequence in context: A019974 A344373 A325873 * A363973 A046781 A244530
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Jun 26 2025
STATUS
approved