A089902 - OEIS

%I #8 Jun 14 2015 01:03:51

%S 1,3,10,40,193,1107,7412,56960,495055,4805327,51540462,605360184,

%T 7726837413,106484488843,1575591323104,24910186990320,419042540060243,

%U 7472730215908551,140804433625595626,2795108750920323336

%N Antidiagonal sums of array A089900.

%C The n-th row of array A089900 is the n-th binomial transform of the factorials found in row 0: {1!,2!,3!,..,(n+1)!,..}. The hyperbinomial transform of the main diagonal gives: {1,4,27,..,(n+1)^(n+1),..}, which is the next lower diagonal in array A089900.

%F a(n) = sum_{k=0..n} sum_{i=0..k} (n-k)^(k-i)*binomial(k, i)*(i+1)!

%F O.g.f.: Sum_{m>=0, n>=1} n!*x^(m+n-1)/(1-m*x)^n - _Vladeta Jovovic_, Nov 18 2003

%o (PARI) a(n)=if(n<0,0,sum(k=0,n,sum(i=0,k,(n-k)^(k-i)*binomial(k,i)*(i+1)!)))

%o (PARI) a(n)=sum(k=0,n,sum(i=0,k,(n-k)^(k-i)*binomial(k,i)*(i+1)!));

%o (PARI) a(n)=polcoeff(sum(m=0,2*n,sum(k=1,2*n,k!*x^(m+k-1)/(1-m*x)^k),x*O(x^n)),n);

%Y Cf. A089900, A089901, A000312.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Nov 14 2003