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 A051740 Partial sums of A007584. 5
 1, 11, 45, 125, 280, 546, 966, 1590, 2475, 3685, 5291, 7371, 10010, 13300, 17340, 22236, 28101, 35055, 43225, 52745, 63756, 76406, 90850, 107250, 125775, 146601, 169911, 195895, 224750, 256680, 291896, 330616, 373065, 419475, 470085, 525141 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Convolution of A000027 with A001106 (excluding 0). - Bruno Berselli, Dec 07 2012 REFERENCES A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196. Murray R.Spiegel, Calculus of Finite Differences and Difference Equations, "Schaum's Outline Series", McGraw-Hill, 1971, pp. 10-20, 79-94. LINKS Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(n) = binomial(n+3, 3)*(7n+4)/4. a(n) = (7*n+4)*binomial(n+3, 3)/4. G.f.: (1+6*x)/(1-x)^5. a(n) = A080852(7,n). - R. J. Mathar, Jul 28 2016 MATHEMATICA f[n_]:=7*n+1; s1=s2=s3=0; lst={}; Do[a=f[n]; s1+=a; s2+=s1; s3+=s2; AppendTo[lst, s3], {n, 0, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jun 25 2009 *) PROG (MAGMA) /* A000027 convolved with A001106 (excluding 0): */ A001106:=func; [&+[(n-i+1)*A001106(i): i in [1..n]]: n in [1..36]]; // Bruno Berselli, Dec 07 2012 CROSSREFS Cf. A001106, A007584. Cf. A093564 ((7, 1) Pascal, column m=4). Cf. A220212 for a list of sequences produced by the convolution of the natural numbers with the k-gonal numbers. Sequence in context: A154106 A232613 A057813 * A263227 A144932 A072262 Adjacent sequences:  A051737 A051738 A051739 * A051741 A051742 A051743 KEYWORD nonn,easy AUTHOR Barry E. Williams, Dec 07 1999 STATUS approved

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Last modified January 21 17:07 EST 2019. Contains 319350 sequences. (Running on oeis4.)