A089902 - OEIS

A089902

Antidiagonal sums of array A089900.

1, 3, 10, 40, 193, 1107, 7412, 56960, 495055, 4805327, 51540462, 605360184, 7726837413, 106484488843, 1575591323104, 24910186990320, 419042540060243, 7472730215908551, 140804433625595626, 2795108750920323336

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OFFSET

0,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..19.

FORMULA

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

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

PROG

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

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

(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);

CROSSREFS

Cf. A089900, A089901, A000312.

Sequence in context: A242651 A231531 A136128 * A093133 A030817 A030845

Adjacent sequences: A089899 A089900 A089901 * A089903 A089904 A089905

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 14 2003

STATUS

approved