Alternating antidiagonal sums of A047920.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =21a(5) =105a(6) =636a(7) =4507a(8) =36449a(9) =330947a(10) =3334302a(11) =36913401a(12) =445422501a(13) =5818511965a(14) =81805201736