A385343 Exponential Riordan array (1, arcsin(x)).

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

Author

Seiichi Manyama, Jun 26 2025

Keywords

• nonn
• tabl

Examples

			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;
		

Crossrefs

Essentialy same as A121408.

Row sums give A006228.

Cf. A091885, A136630, A185951.

Programs

PARI

T(n, k) = my(x='x+O('x^(n+1))); n!*polcoef(asin(x)^k/k!, n);

Formula

E.g.f. of column k (with leading zeros): arcsin(x)^k / k!

T(n,k) = A121408(n,k) for k > 0.