A217485 Convolution of the numbers in sequence A080253.

1, 6, 43, 396, 4565, 64146, 1073919, 20996376, 471081385, 11947911966, 338204687315, 10570101018276, 361458024882045, 13421571912745386, 537661560385125031, 23108777539028187696, 1060571767117824260945, 51760585513634983767606

Offset: 0

Author

Emanuele Munarini, Oct 04 2012

Keywords

• nonn

Crossrefs

Cf. A080253, A000670, A217483, A217484, A217486, A217487, A217488.

Programs

Mathematica

t[n_] := Sum[StirlingS2[n, k] k!, {k, 0, n}]; c[n_] := Sum[Binomial[n, k] 2^k t[k], {k, 0, n}]; Table[Sum[c[k]c[n-k], {k,0,n}], {n,0,100}]

Maxima

t(n):=sum(stirling2(n,k)*k!,k,0,n);
c(n):=sum(binomial(n,k)*2^k*t(k),k,0,n);
makelist(sum(c(k)*c(n-k),k,0,n),n,0,40);

Formula

a(n) = sum(c(k)*c(n.k),k=0..n), where c(n) = A080253(n).

a(n) ~ n! * 2^(n + 1/2) / (log(2))^(n+1). - Vaclav Kotesovec, Nov 27 2017