0,5

E.g.f. A(x)=y satisfies (y+y'+y'')y-y'^2=0. - Michael Somos Mar 11 2004

The 10-adic sum: B(n) = Sum_{k>=0} k^n*k! simplifies to: B(n) = A014182(n)*B(0) + A014619(n) for n>=0, where B(0) is the 10-adic sum of factorials (A025016); a result independent of base. - Paul D. Hanna (pauldhanna(AT)juno.com), Aug 12 2006

Equals row sums of triangle A143987 and (shifted) = right border of A143987. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 07 2008]

Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 31 2008: (Start)

Equals the eigensequence of the inverse of Pascal's triangle, A007318.

Binomial transform shifts to the right: (1, 1, 0, -1, 1, 2, -9,...).

Double binomial transform = A109747 (End)

Convolved with A154107 = A000110, the Bell numbers. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 04 2009]

E.g.f.: exp(1-x-exp(-x)).

a(n) = Sum_{k=0..n} (-1)^(n-k)*Stirling2(n+1,k+1). - Paul D. Hanna (pauldhanna(AT)juno.com), Aug 12 2006

(PARI) {a(n)=sum(j=0, n, (-1)^(n-j)*Stirling2(n+1, j+1))} /* Stirling2 defined by: */ {Stirling2(n, k)=(1/k!)*sum(i=0, k, (-1)^(k-i)*binomial(k, i)*i^n)} - Paul D. Hanna (pauldhanna(AT)juno.com), Aug 12 2006

(PARI) {a(n)=if(n<0, 0, n!*polcoeff( exp( 1-x-exp( -x+x*O(x^n))), n))} /* Michael Somos Mar 11 2004 */

Essentially same as A000587. See also A014619.

Cf. A025016.

A143987 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 07 2008]

A109747 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 31 2008]

A154107, A000110 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 04 2009]

Sequence in context: A003678 A109322 A000587 this_sequence A131463 A065644 A043065

Adjacent sequences: A014179 A014180 A014181 this_sequence A014183 A014184 A014185

sign,easy,nice

Noam Elkies (elkies(AT)math.harvard.edu)