A321961 Sums of antidiagonals of A321964.

1, 1, 2, 6, 29, 205, 1900, 21592, 289325, 4456773, 77512394, 1501537750, 32053808641, 747561173689, 18911411905052, 515798244940224, 15088848988966409, 471291927943037785, 15655172277281565058, 551102758946418279862, 20495154400760992784213, 802951447375696586076213

Offset: 0

Author

Peter Luschny, Dec 27 2018

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A321964.

Programs

Sage

def A321961List(l):
    def row(n, dim):
        m = 1
        for k in range(dim-1, -1, -1):
            m = 1 - (n+k)*x/m
        return SR(1/m).series(x, dim).list()
    return [sum(row(n-k, n+1)[k] for k in (0..n)) for n in (0..l-1)]
A321961List(16)

Formula

a(n) ~ 2^(n - 1/2) * n^(n-1) / exp(n-1). - Vaclav Kotesovec, Jan 06 2019