A291214 Column 2 of triangle A290580.

1, 112, 5868, 250128, 10020912, 399379728, 16255733440, 684615750832, 30031767680256, 1376568893633760, 66017645596167168, 3313241694194681184, 173934275433107845120, 9543378596912872361440, 546711252967087466397696, 32663132242303127521217184

Offset: 1

Author

Vaclav Kotesovec, Aug 21 2017

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..77

Crossrefs

Cf. A290580, A290581.

Programs

PARI

/* As column 2 of triangle A290580 */
{ A290580(n, k) = my(W=1, E=1, S=x, C=1, D=1); for(i=0, n,
S = intformal(C*D +x*O(x^n)) ;
C = 1 - intformal(S*D) ; D = 1 - m*intformal(S*C) ;
E = subst( (1 + S)/C, m, 1-m) ) ;
for(i=0, n, W = subst(E, x, x*W));
n!*polcoeff(polcoeff(W, n, x), k, m) }
for(n=1, 25, print1( A290580(n+4, 2), ", ")) \\ after Paul D. Hanna

Formula

a(n) ~ c * n^(n+5), where c = (exp(1) + 8*exp(3) + 14*exp(5) - 8*exp(7) + exp(9))/512 = 3.06876067343310165753640903985063833178947434...