A363042 Row sums of A363041.
1, 1, 2, 6, 17, 57, 233, 989, 4602, 23794, 129285, 751973, 4680041, 30523105, 210159654, 1521122754, 11481486845, 90604333205, 744420806913, 6348340033789, 56202980961206, 514994183598470, 4877587872447801, 47711923353493817, 481072714151555073, 4995769099914083313
Offset: 1
Programs
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Maple
seq(add( Stirling2(n+1,n-2*k)/binomial(n-2*k+1,2), k = 0..floor((n-1)/2) ), n = 1..30);
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PARI
a(n) = sum(k = 0, (n-1)\2, stirling(n+1, n-2*k, 2)/binomial(n-2*k+1, 2)); \\ Michel Marcus, May 21 2023
Formula
a(n) = Sum_{k = 0..floor((n-1)/2)} Stirling2(n+1,n-2*k)/binomial(n-2*k+1,2).