A294253 E.g.f.: exp((1+x)*(1+x^2)*(1+x^3)*(1+x^4)*(1+x^5) - 1).

1, 1, 3, 19, 121, 1041, 9931, 106723, 1313649, 17830081, 265652371, 4259421651, 74011854313, 1374298028689, 27230459440731, 573414615381091, 12723857450638561, 297915550887491073, 7328943525355675939, 188820746254730967571, 5086439179764958688601

Offset: 0

Author

Seiichi Manyama, Oct 26 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..446

Crossrefs

Column k=5 of A294250.

Cf. A294216.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Exp[Times@@(1+x^Range[5])-1],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 16 2023 *)

PARI

N=66; x='x+O('x^N); Vec(serlaplace(exp((1+x)*(1+x^2)*(1+x^3)*(1+x^4)*(1+x^5)-1)))

Formula

Recurrence: a(n) = a(n-1) + 2*(n-1)*a(n-2) + 6*(n-2)*(n-1)*a(n-3) + 8*(n-3)*(n-2)*(n-1)*a(n-4) + 15*(n-4)*(n-3)*(n-2)*(n-1)*a(n-5) + 18*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-6) + 21*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-7) + 24*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-8) + 27*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-9) + 30*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n - 10) + 22*(n - 10)*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n - 11) + 24*(n - 11)*(n - 10)*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n - 12) + 13*(n - 12)*(n - 11)*(n - 10)*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n - 13) + 14*(n - 13)*(n - 12)*(n - 11)*(n - 10)*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n - 14) + 15*(n - 14)*(n - 13)*(n - 12)*(n - 11)*(n - 10)*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n - 15). - Vaclav Kotesovec, Dec 02 2021