A381107 Expansion of e.g.f. -log(1-x) * (exp(x) - 1) / (1-x).

0, 0, 2, 12, 66, 395, 2665, 20307, 173488, 1646745, 17216653, 196730567, 2440331300, 32666847941, 469457190501, 7210003071247, 117862325748960, 2043420738374545, 37453428525580725, 723643767046525111, 14700326905250293556, 313236372986056228013, 6985951253209713959645

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = Sum_{k=0..n-1} binomial(n,k) * |Stirling1(k+1,2)|.

a(n) = A073596(n) - A000254(n).

Prog

(PARI) a(n) = sum(k=0, n-1, binomial(n, k)*abs(stirling(k+1, 2, 1)));

Crossrefs

Cf. A002627, A381108.

Cf. A000254, A073596.

Sequence in context: A323925 A039633 A265451 * A180195 A377507 A212389

Adjacent sequences: A381104 A381105 A381106 * A381108 A381110 A381111

Keyword

nonn,new

Author

Seiichi Manyama, Feb 14 2025

Status

approved