A124527 Row sums of triangle A124526.

1, 1, 2, 5, 14, 46, 162, 641, 2656, 12092, 56956, 290636, 1523088, 8559980, 49163792, 300514337, 1870652672, 12318376190, 82394305842, 580168452664, 4141242464512, 30992978322024, 234765130286990, 1858132080028884

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Maple

b:= proc(n, k) option remember; `if`(k<0 or k>n, 0,
      `if`(n=0, 1, b(n-1, k-1) +(k+1)*(b(n-1, k) +b(n-1, k+1))))
    end:
a:= n-> add(b(iquo(n, 2), k)*b(iquo(n+1, 2), k), k=0..n/2):
seq(a(n), n=0..30);  # Alois P. Heinz, Apr 14 2014

Mathematica

b[n_, k_] := b[n, k] = If[k < 0 || k > n, 0, If[n == 0, 1, b[n - 1, k - 1] + (k + 1) (b[n - 1, k] + b[n - 1, k + 1])]];
a[n_] := Sum[b[Quotient[n, 2], k] b[Quotient[n + 1, 2], k], {k, 0, n/2}];
a /@ Range[0, 30]
(* Second program: *)
S[n_, k_] = Sum[StirlingS2[n, i] Binomial[i, k], {i, 0, n}];
T[n_, k_] := S[Floor[n/2], k] S[Floor[(n + 1)/2], k];
a[n_] := Sum[T[n, k], {k, 0, Floor[n/2]}];
a /@ Range[0, 30] (* Jean-François Alcover, Nov 02 2020, first program after Alois P. Heinz *)

Prog

(PARI) {a(n)=sum(k=0, n\2, (n\2)!*((n+1)\2)!*polcoeff(polcoeff(exp((1+y)*(exp(x+x*O(x^n))-1)), n\2), k) *polcoeff(polcoeff(exp((1+y)*(exp(x+x*O(x^n))-1)), (n+1)\2), k))}

Crossrefs

Cf. A124526; A124528, A124529.

Sequence in context: A149895 A149896 A149897 * A149898 A240611 A240612

Adjacent sequences: A124524 A124525 A124526 * A124528 A124529 A124530

Keyword

nonn

Author

Paul D. Hanna, Nov 08 2006

Status

approved